{"id":5208,"date":"2023-08-11T14:24:42","date_gmt":"2023-08-11T13:24:42","guid":{"rendered":"http:\/\/mosaic-modeling.de\/?page_id=5208"},"modified":"2024-07-14T15:23:47","modified_gmt":"2024-07-14T14:23:47","slug":"use-of-optimizations-minlp-example","status":"publish","type":"page","link":"https:\/\/mosaic-modeling.de\/?page_id=5208","title":{"rendered":"Use of Optimizations I &#8211; MINLP Example"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">On this page<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Synthesis-problem\" >Synthesis problem<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Model-description\" >Model description<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Modeling-Workflow\" >Modeling Workflow<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Notation-of-equation-system\" >Notation of equation system<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Base-names\" >Base names<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Superscripts\" >Superscripts<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Indices\" >Indices<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Equations\" >Equations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Equation-system\" >Equation system<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Simulation-workflow\" >Simulation workflow<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Optimization-workflow\" >Optimization workflow<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Constraints\" >Constraints<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Variable-specification\" >Variable specification<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Code-generation-and-solution\" >Code generation and solution<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5208\/#Results\" >Results<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p style=\"text-align: justify;\">This tutorial explains how a simple process synthesis problem can be set up and solved. This synthesis problem results in an mixed-integer nonlinear programming problem.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Synthesis-problem\"><\/span>Synthesis problem<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The synthesis problem contains two options (process I and II) to produce B from A. These processes vary in their fixed and variable costs. In addition, there is the option to simply purchase B directly. Whatever the source of B is, all streams are mixed in a mixer (streams 2, 4, and 5). In the final step, any B is converted to C via process III.<\/p>\n<figure id=\"attachment_5233\" aria-describedby=\"caption-attachment-5233\" style=\"width: 832px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/MINLP-Example.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-5233\" src=\"http:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/MINLP-Example.png\" alt=\"\" width=\"832\" height=\"271\" srcset=\"https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/MINLP-Example.png 832w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/MINLP-Example-300x98.png 300w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/MINLP-Example-768x250.png 768w\" sizes=\"auto, (max-width: 832px) 100vw, 832px\" \/><\/a><figcaption id=\"caption-attachment-5233\" class=\"wp-caption-text\">Figure 1: Superstructure for process synthesis example.<\/figcaption><\/figure>\n<h3><span class=\"ez-toc-section\" id=\"Model-description\"><\/span>Model description<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">This example is governed by the following equations:<\/p>\n<p><p class=\"ql-left-displayed-equation\" style=\"line-height: 153px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-8f4531a993f8b047fd801872173777e3_l3.png\" height=\"153\" width=\"433\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#108;&#105;&#103;&#110;&#42;&#125;&#38;&#70;&#95;&#123;&#115;&#61;&#50;&#44;&#99;&#125;&#32;&#61;&#32;&#70;&#95;&#123;&#115;&#61;&#49;&#44;&#99;&#125;&#32;&#43;&#32;&#82;&#95;&#99;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#119;&#101;&#100;&#103;&#101;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#82;&#95;&#99;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;&#32;&#61;&#32;&#92;&#110;&#117;&#95;&#99;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;&#32;&#114;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;&#32;&#92;&#108;&#110;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#32;&#49;&#32;&#43;&#32;&#70;&#95;&#123;&#115;&#61;&#49;&#44;&#99;&#61;&#49;&#125;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#92;&#92;&#091;&#50;&#101;&#120;&#093;&#38;&#70;&#95;&#123;&#115;&#61;&#52;&#44;&#99;&#125;&#32;&#61;&#32;&#70;&#95;&#123;&#115;&#61;&#51;&#44;&#99;&#125;&#32;&#43;&#32;&#82;&#95;&#99;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#119;&#101;&#100;&#103;&#101;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#82;&#95;&#99;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;&#32;&#61;&#32;&#92;&#110;&#117;&#95;&#99;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;&#32;&#114;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;&#32;&#92;&#108;&#110;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#32;&#49;&#32;&#43;&#32;&#70;&#95;&#123;&#115;&#61;&#51;&#44;&#99;&#61;&#49;&#125;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#92;&#92;&#091;&#50;&#101;&#120;&#093;&#38;&#70;&#95;&#123;&#115;&#61;&#55;&#44;&#99;&#125;&#32;&#61;&#32;&#70;&#95;&#123;&#115;&#61;&#54;&#44;&#99;&#125;&#32;&#43;&#32;&#82;&#95;&#99;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#119;&#101;&#100;&#103;&#101;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#82;&#95;&#99;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;&#32;&#61;&#32;&#92;&#110;&#117;&#95;&#99;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;&#32;&#114;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;&#32;&#70;&#95;&#123;&#115;&#61;&#54;&#44;&#99;&#61;&#50;&#125;&#32;&#92;&#92;&#091;&#50;&#101;&#120;&#093;&#38;&#70;&#95;&#123;&#115;&#61;&#54;&#44;&#99;&#125;&#32;&#61;&#32;&#70;&#95;&#123;&#115;&#61;&#50;&#44;&#99;&#125;&#32;&#43;&#32;&#70;&#95;&#123;&#115;&#61;&#52;&#44;&#99;&#125;&#32;&#43;&#32;&#70;&#95;&#123;&#115;&#61;&#53;&#44;&#99;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#108;&#105;&#103;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/p>\n<p>The first part of each equation is the component balance for the three processes. The second part determines the conversion in each process. Therein, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5376f6867c11bfe62d1de72e3207e7cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"\/> is the stoichiometric coefficient and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> is a conversion coefficient. The conversion always depends on the educt feed to the respective process. Finally, there is a component balance for the mixer.<\/p>\n<p>In addition, there are logical \/ structural constraints:<\/p>\n<p><p class=\"ql-left-displayed-equation\" style=\"line-height: 158px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ccda9035de6005b87e9b50da486b05bd_l3.png\" height=\"158\" width=\"348\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#108;&#105;&#103;&#110;&#42;&#125;&#38;&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;&#32;&#43;&#32;&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;&#32;&#61;&#32;&#99;&#95;&#123;&#105;&#61;&#49;&#125;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#119;&#101;&#100;&#103;&#101;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#99;&#95;&#123;&#105;&#61;&#49;&#125;&#32;&#92;&#108;&#101;&#113;&#32;&#49;&#32;&#92;&#92;&#091;&#50;&#101;&#120;&#093;&#38;&#70;&#95;&#123;&#115;&#61;&#50;&#44;&#99;&#61;&#50;&#125;&#32;&#45;&#32;&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;&#32;&#70;&#95;&#123;&#115;&#61;&#50;&#44;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#109;&#97;&#120;&#125;&#32;&#61;&#32;&#99;&#95;&#123;&#105;&#61;&#50;&#125;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#119;&#101;&#100;&#103;&#101;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#99;&#95;&#123;&#105;&#61;&#50;&#125;&#32;&#92;&#108;&#101;&#113;&#32;&#48;&#32;&#92;&#92;&#091;&#50;&#101;&#120;&#093;&#38;&#70;&#95;&#123;&#115;&#61;&#52;&#44;&#99;&#61;&#50;&#125;&#32;&#45;&#32;&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;&#32;&#70;&#95;&#123;&#115;&#61;&#52;&#44;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#109;&#97;&#120;&#125;&#32;&#61;&#32;&#99;&#95;&#123;&#105;&#61;&#51;&#125;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#119;&#101;&#100;&#103;&#101;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#99;&#95;&#123;&#105;&#61;&#51;&#125;&#32;&#92;&#108;&#101;&#113;&#32;&#48;&#32;&#92;&#92;&#091;&#50;&#101;&#120;&#093;&#38;&#70;&#95;&#123;&#115;&#61;&#55;&#44;&#99;&#61;&#51;&#125;&#32;&#45;&#32;&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;&#32;&#70;&#95;&#123;&#115;&#61;&#55;&#44;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#109;&#97;&#120;&#125;&#32;&#61;&#32;&#99;&#95;&#123;&#105;&#61;&#52;&#125;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#119;&#101;&#100;&#103;&#101;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#99;&#95;&#123;&#105;&#61;&#52;&#125;&#32;&#92;&#108;&#101;&#113;&#32;&#48;&#92;&#101;&#110;&#100;&#123;&#97;&#108;&#105;&#103;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/p>\n<p style=\"text-align: justify;\">The first constraint ensures that either process I or process II is used, but not both. The other three constraints ensure that the produced product in processes I, II, and III is below the maximum capacity of each process. The processes are activated by the binary decision variables <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-582510931040302a95a28c75bbcad009_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"14\" style=\"vertical-align: -4px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ee40f667c749b286d269c811cd940868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"20\" style=\"vertical-align: -4px;\"\/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-729e5ed3efed705273b5aea483c0d8a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\"\/>.<\/p>\n<p>Last but not least, the objective function must be formulated. The synthesized process shall be the most cost-efficient option:<\/p>\n<p><p class=\"ql-left-displayed-equation\" style=\"line-height: 22px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-b1b4425c7c3a2a151c608bcff430f49a_l3.png\" height=\"22\" width=\"1166\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;&#92;&#80;&#104;&#105;&#32;&#61;&#32;&#67;&#94;&#123;&#73;&#44;&#102;&#105;&#120;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#94;&#123;&#73;&#125;&#32;&#43;&#32;&#67;&#94;&#123;&#73;&#73;&#44;&#102;&#105;&#120;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#94;&#123;&#73;&#73;&#125;&#32;&#43;&#32;&#67;&#94;&#123;&#73;&#73;&#73;&#44;&#102;&#105;&#120;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#94;&#123;&#73;&#73;&#73;&#125;&#43;&#32;&#67;&#94;&#123;&#73;&#44;&#118;&#97;&#114;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#70;&#95;&#123;&#115;&#61;&#50;&#44;&#99;&#61;&#50;&#125;&#32;&#43;&#32;&#67;&#94;&#123;&#73;&#73;&#44;&#118;&#97;&#114;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#70;&#95;&#123;&#115;&#61;&#52;&#44;&#99;&#61;&#50;&#125;&#32;&#43;&#32;&#67;&#94;&#123;&#73;&#73;&#73;&#44;&#118;&#97;&#114;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#70;&#95;&#123;&#115;&#61;&#55;&#44;&#99;&#61;&#51;&#125;&#43;&#32;&#67;&#94;&#123;&#118;&#97;&#114;&#125;&#95;&#123;&#99;&#61;&#49;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#40;&#70;&#95;&#123;&#115;&#61;&#49;&#44;&#99;&#61;&#49;&#125;&#43;&#70;&#95;&#123;&#115;&#61;&#51;&#44;&#99;&#61;&#49;&#125;&#41;&#32;&#43;&#32;&#67;&#94;&#123;&#118;&#97;&#114;&#125;&#95;&#123;&#99;&#61;&#50;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#70;&#95;&#123;&#115;&#61;&#53;&#44;&#99;&#61;&#50;&#125;&#32;&#45;&#32;&#67;&#94;&#123;&#118;&#97;&#114;&#125;&#95;&#123;&#99;&#61;&#51;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#70;&#95;&#123;&#115;&#61;&#55;&#44;&#99;&#61;&#51;&#125;&#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/p>\n<p>Hence, the objective function is the sum of fix and variable costs of all processes. The variable costs are only associated with the product stream in this simple example. The last terms represent the costs for educts that must be paid for streams 1, 3, and 5. The objective function is reduced by the income generated by selling the product in stream 7. The binary variables activate these terms in the cost function.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Modeling-Workflow\"><\/span>Modeling Workflow<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"Notation-of-equation-system\"><\/span>Notation of equation system<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>For the notation of the equation, we need to set up all base names, superscripts, and indices that appear in the equations, i.e.<\/p>\n<h5><span class=\"ez-toc-section\" id=\"Base-names\"><\/span>Base names<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5376f6867c11bfe62d1de72e3207e7cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"\/>, stoichiometric coefficient<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-21f36758b04341c7980aa18b13ced720_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#80;&#104;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/>, objective function value<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>, constraint dummy<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ed12970f60569db1dfd9f13289854a0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/>, cost in EURO<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-88df03c55e081c7cd9da4e7d74ba7265_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/>, mass flow in t\/h<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>, conversion coefficient<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-d6abdd487c56e5efbb2c9522ed4b9360_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/>, conversion in t\/h<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-38461fc041e953482219abf5d4cce1cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"\/>, binary decision variable<\/li>\n<\/ul>\n<h5><span class=\"ez-toc-section\" id=\"Superscripts\"><\/span>Superscripts<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li>fix, fixed cost<\/li>\n<li>I, process I<\/li>\n<li>II, process II<\/li>\n<li>III, process III<\/li>\n<li>max, maximum<\/li>\n<li>var, variable cost<\/li>\n<\/ul>\n<h5><span class=\"ez-toc-section\" id=\"Indices\"><\/span>Indices<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>, component index 1..NC<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-31318c5dcb226c69e0818e5f7d2422b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"\/>, constraint index 1..NI<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>, stream index 1..NS<\/li>\n<\/ul>\n<p>The resulting notation has ID 182686.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Equations\"><\/span>Equations<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\">Next, we can define the equations of the model. Therefore, we open the equation editor, load the notation we just created, and enter the equations as stated above in the model description. The formulated equations are available with the IDs 182688 to 182698 (11 equations). The objective function has ID 182700.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Equation-system\"><\/span>Equation system<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\">Now we are able to construct our equation system:<\/p>\n<ol>\n<li style=\"text-align: justify;\">Go to &#8220;Equation System&#8221; and load the notation for the equations<\/li>\n<li>Add the eleven constraints and the objective function to your system in the Connected Elements tab<\/li>\n<li>Save your equation system<\/li>\n<\/ol>\n<p>This equation system is available with ID 182699.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Simulation-workflow\"><\/span>Simulation workflow<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Your model is now complete and you can move on to the &#8220;Simulation&#8221; section of MOSAICmodeling.<\/p>\n<ol style=\"text-align: justify;\">\n<li>Enter a suitable description<\/li>\n<li>Select the tab Equation System and load the system created in the previous steps. Assign the maximum values for the available indices (NC = 3,\u00a0NI = 4, NS = 7)\u00a0and click on Confirm Index Data<\/li>\n<li>Select the tab Specifications. In the list ALL VARIABLES, you will find the variables as defined in your model notation.<\/li>\n<li>Classify the variables as design variables and iteration values, respectively, by selecting the category from the dropdown menu in the Type column.<\/li>\n<\/ol>\n<p>The simulation will be specified and initialized with the values given in Table 1. After having assigned the initial guesses and the parameter values, you can save the variable specification and then the simulation. The simulation is available in MOSAICmodeling with ID 182704. The respective variable specification that may serve as initialization for the optimization has ID 182705. The solution for both iteration variables and both cases is also given in Table 1. In this case, the solution is equal to the initial guesses, which basically shows that the system is well initialized for optimization.<\/p>\n\n\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Name<\/th><th class=\"has-text-align-left\" data-align=\"left\">Description<\/th><th class=\"has-text-align-left\" data-align=\"left\">Value \/ Initial guess<\/th><th class=\"has-text-align-left\" data-align=\"left\">Solution<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-e62b19e3672f99cfb4979626c721c80e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"32\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 1 in process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">-1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-2b606f1aea098a3c16a697fac3a02b64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"33\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 2 in process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-9ee7b94579cfa0be079fe535bafe3beb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"33\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 3 in process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-2b7be6db0e51dc82339b79da701882a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"32\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 1 in process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">-1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-974e54271401478cf490b49ac7a45ce1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"33\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 2 in process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-649a1afb4ba0ac08b7fefc52c56053ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"33\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 3 in process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-b58549b5482a3d9a7d725463446bd78a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"32\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 1 in process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-fd48bb795edb977e13ddef10de7fe9fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"33\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 2 in process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">-1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-93c0281118f4f80d3715960ea6fe8721_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"33\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 3 in process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-65d8d47d4329484c62443ecfb95a4a27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#44;&#32;&#102;&#105;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"39\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Fix costs of process I in \u20ac\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">1000<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-47ff26e562893bf9fe46d12df9a85bac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#44;&#32;&#102;&#105;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"44\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Fix costs of process II in \u20ac\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">1500<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-8425754ddb571d5a497ede40e20e6b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#44;&#32;&#102;&#105;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Fix costs of process III in \u20ac\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">3500<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-8bd3cac7b7c0eba82b4e2d21fc039c87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#44;&#32;&#118;&#97;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"41\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Variable costs of process I in \u20ac\/t<\/td><td class=\"has-text-align-left\" data-align=\"left\">1000<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-00859e5d6a2240adc5b57ab6a23c5282_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#44;&#32;&#118;&#97;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"47\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Variable costs of process II in \u20ac\/t<\/td><td class=\"has-text-align-left\" data-align=\"left\">1200<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5529d233991ee3941c1b910ea04b94d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#44;&#32;&#118;&#97;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"52\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Variable costs of process III in \u20ac\/t<\/td><td class=\"has-text-align-left\" data-align=\"left\">2000<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-4f53e2d3670c8d7a93fc1c97c85f1e3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#118;&#97;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"36\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Costs for component 1<\/td><td class=\"has-text-align-left\" data-align=\"left\">1800<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-2c00f90b9aa8b748fe89931b875e8aee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#118;&#97;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Costs for component 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">7000<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-e88eef09524dca7ab0da876429db11b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#118;&#97;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Selling price for component 3<\/td><td class=\"has-text-align-left\" data-align=\"left\">13000<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ec56d95c4b98b4654b91c271906106fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#49;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 1 in stream 1 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-8659ade4316a7544ca3282fb34fc6a12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#51;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 1 in stream 3 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-c9bb28c4dcb94c3d06820a4885160daf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#53;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 1 in stream 5 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5635cff1b9b3c4e3e4871d3433c1caff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#49;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 2 in stream 1 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-16c6b858e62b2ed96f0e30daa7b7a136_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#51;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 2 in stream 3 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-6a32d8e31cc93edc167e9830f0bec1e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#53;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 2 in stream 5 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">2<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-83b558675dd4880dd7070e39057e7fdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#49;&#44;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 3 in stream 1 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-8bf73791eea8780936e57fba34217f3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#51;&#44;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 3 in stream 3 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-fe9d1ddc5eff83dbf2195a5e0b6d9245_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#53;&#44;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 3 in stream 5 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ecafafd795dc5dc2038aa46f7d5b4348_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#50;&#44;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#109;&#97;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"63\" style=\"vertical-align: -8px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Maximum capacity of process I in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">4<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-06ec4252a6480e3b82ddcbf2c4a728bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#52;&#44;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#109;&#97;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"63\" style=\"vertical-align: -8px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Maximum capacity of process II in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">5<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-349776e91eda1d8957c61afc96a491c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#55;&#44;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#109;&#97;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"63\" style=\"vertical-align: -8px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Maximum capacity of process III in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">2<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-d43a11eac7cda5c8ef718ed32dd2a226_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"13\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion factor of process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-986742493fcdfd5fcd8de474807bfa56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"19\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion factor of process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.2<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-95b344d23e86051d7861eb8d3abbec2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion factor of process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.9<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-582510931040302a95a28c75bbcad009_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"14\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Binary decision variable for process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ee40f667c749b286d269c811cd940868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"20\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Binary decision variable for process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-729e5ed3efed705273b5aea483c0d8a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Binary decision variable for process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-9853456abd3977c798a303b561cd8a94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#50;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 1 in stream 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-033dfad79a496729a0f7b534339281ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#52;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 1 in stream 4<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-1fab306bef61358620b5e541a201f9ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#54;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 1 in stream 6<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-247efbca2137f6e6135a3526a9695583_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#55;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 1 in stream 7<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-6666fae5a5e443513ba2a00b01da2762_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#50;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 2 in stream 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-cf568603bab2698b8aa0fcf756e86ab9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#52;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 2 in stream 4<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-4c191936fcc91175bf0dc42d8311436c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#54;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 2 in stream 6<\/td><td class=\"has-text-align-left\" data-align=\"left\">2<\/td><td class=\"has-text-align-left\" data-align=\"left\">2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-1445a90e58ffb4ab04bc269c4206a7da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#55;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 2 in stream 7<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-41488209a626989354a722428b5ba1bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#50;&#44;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 3 in stream 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-3f9f3b2eb96b04de84b9dea8e008fe80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#52;&#44;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 3 in stream 4<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-65b6c8eabfecc3454feb512f8bc62a88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#54;&#44;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 3 in stream 6<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ec481b59f299e1d93718ac187cc34c57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#55;&#44;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 3 in stream 7<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.8<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.8<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-850f61e9dbafe507321352b867fa6abe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"36\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 1 in process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-b26fac04490dff5733240060d5d264c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 2 in process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-7cb82c64e82323d797a3eb7e26ed1fb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 3 in process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-133a85804afb9ae0a545b9b8c8fd4e2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"36\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 1 in process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-f4a33272aecdef68c3da63594378949e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 2 in process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ebc35e089e1be296d0ec09ea81ff4829_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 3 in process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-78c80509a5947d7725d7595bd1098eaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"36\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 1 in process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-d54528052cd1f26d7632b9202e6f3b4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 2 in process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">-1.8<\/td><td class=\"has-text-align-left\" data-align=\"left\">-1.8<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-79ba30e6224f34fc1325d9d01e9b4bbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 3 in process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.8<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.8<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-f1bab0cd523067587582231ae6904381_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#105;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"30\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Dummy variable 1<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-6b40bfeb7eb890ecbe7e770b857a2d9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#105;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"31\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Dummy variable 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-b981e8796ec537002212d01015407c0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#105;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"31\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Dummy variable 3<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-cf24d34e601f159d0864d7cd8c37da9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#105;&#61;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"31\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Dummy variable 4<\/td><td class=\"has-text-align-left\" data-align=\"left\">-0.2<\/td><td class=\"has-text-align-left\" data-align=\"left\">-0.2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-21f36758b04341c7980aa18b13ced720_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#80;&#104;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Objective function value<\/td><td class=\"has-text-align-left\" data-align=\"left\">-2300<\/td><td class=\"has-text-align-left\" data-align=\"left\">-2300<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 1: Overview of design values and initial guesses.<\/figcaption><\/figure>\n\n\n<h3><span class=\"ez-toc-section\" id=\"Optimization-workflow\"><\/span>Optimization workflow<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Now that the system is well initialized, move to the &#8220;Optimization&#8221; section in MOSAICmodeling and go to the Specification tab.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Constraints\"><\/span>Constraints<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Go to the Constraints tab and load your simulation from the previous step. Make sure that all eleven constraints and the objective function are loaded successfully.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Variable-specification\"><\/span>Variable specification<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Go to the Variable specification. If you saved the simulation after you saved the variable specification, the variable specification from the simulation should be loaded in the optimization as well.<\/p>\n<ol>\n<li>Start by assigning <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-21f36758b04341c7980aa18b13ced720_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#80;&#104;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/> as objective value.<\/li>\n<li>Then assign the variables in Table 2 as optimization values and set the given lower and upper bounds. If a value is missing, there is no bound to consider and you can set an arbitrarily high or small value. In addition, define <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-582510931040302a95a28c75bbcad009_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"14\" style=\"vertical-align: -4px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ee40f667c749b286d269c811cd940868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"20\" style=\"vertical-align: -4px;\"\/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-729e5ed3efed705273b5aea483c0d8a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\"\/> as integer.<\/li>\n<li>You can now save the variable specification &#8211; either by overwriting the one from your simulation or by creating a new one. The resulting variable specification with the updated\u00a0 type classifications and variable bounds has ID 182706.<\/li>\n<li>Save the optimization (ID of optimization with this example: 182707).<\/li>\n<\/ol>\n\n\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Name<\/th><th class=\"has-text-align-center\" data-align=\"center\">Lower bound<\/th><th class=\"has-text-align-center\" data-align=\"center\">Upper bound<\/th><th class=\"has-text-align-center\" data-align=\"center\">Integer?<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ec56d95c4b98b4654b91c271906106fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#49;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-8659ade4316a7544ca3282fb34fc6a12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#51;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-6a32d8e31cc93edc167e9830f0bec1e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#53;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-f1bab0cd523067587582231ae6904381_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#105;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"30\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-6b40bfeb7eb890ecbe7e770b857a2d9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#105;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"31\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-b981e8796ec537002212d01015407c0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#105;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"31\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-cf24d34e601f159d0864d7cd8c37da9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#105;&#61;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"31\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-582510931040302a95a28c75bbcad009_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"14\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">Yes<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ee40f667c749b286d269c811cd940868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"20\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">Yes<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-729e5ed3efed705273b5aea483c0d8a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">Yes<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 2: Variable bounds for the optimization.<\/figcaption><\/figure>\n\n\n<h4><span class=\"ez-toc-section\" id=\"Code-generation-and-solution\"><\/span>Code generation and solution<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Go to the Code Generation &amp; Execution tab. This tab offers two possibilities:<\/p>\n<ol>\n<li>Code generation for use on a local machine<\/li>\n<li>Code generation and execution on the NEOS server<\/li>\n<\/ol>\n<p>We take the second option by opening the Code Generation &amp; Execution on NEOS Server tab. First, you need to click on Accept &amp; Connect at the bottom to accept the terms of use.<\/p>\n<p>Go to the Submit tab and take the following steps:<\/p>\n<ol>\n<li>Select Mixed Integer Nonlinearly Constrained Optimization as Category<\/li>\n<li>Select BONMIN as Solver (you need to actually click on it before Language can be selected)<\/li>\n<li>Select AMPL as Language<\/li>\n<li>Click on Generate Code &amp; Submit<\/li>\n<\/ol>\n<p>Go to the tab History. If the job does not appear in your history, click on &#8220;Refresh&#8221;. Once the status is &#8220;Done&#8221;, you can click on the job and scroll down to the results.<\/p>\n<p>You can copy these results and re-import them into MOSAICmodeling by doing the following:<\/p>\n<ol>\n<li>In the Specification tab, go to the Variable Specification tab and click on &#8220;Import Values&#8221;<\/li>\n<li>Paste the results into this window and select AMPL as Language Specification (at the top). You can click on &#8220;Test Import&#8221; to see whether the variables are correctly recognized.<\/li>\n<li>Click on Import. This updates all variable values in your variable specification.\u00a0<\/li>\n<li>If you want to, you can save this new variable specification with another name, e.g., &#8220;Results&#8221;<\/li>\n<\/ol>\n<h4><span class=\"ez-toc-section\" id=\"Results\"><\/span>Results<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>The results obtained with BONMIN are given below in Table 3. Values that were numerically zero are shown as 0\u00a0 for clarity. The results indicate that the best option under the current constraint is using process II and buying additional B, which is then used to produce C. The variable specification containing the results has ID 182729.<\/p>\n\n\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Name<\/th><th class=\"has-text-align-left\" data-align=\"left\">Description<\/th><th class=\"has-text-align-left\" data-align=\"left\">Value \/ Initial guess<\/th><th class=\"has-text-align-left\" data-align=\"left\">Solution<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-e62b19e3672f99cfb4979626c721c80e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"32\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 1 in process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">-1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-2b606f1aea098a3c16a697fac3a02b64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"33\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 2 in process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-9ee7b94579cfa0be079fe535bafe3beb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"33\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 3 in process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-2b7be6db0e51dc82339b79da701882a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"32\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 1 in process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">-1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-974e54271401478cf490b49ac7a45ce1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"33\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 2 in process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-649a1afb4ba0ac08b7fefc52c56053ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"33\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 3 in process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-b58549b5482a3d9a7d725463446bd78a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"32\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 1 in process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-fd48bb795edb977e13ddef10de7fe9fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"33\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 2 in process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">-1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-93c0281118f4f80d3715960ea6fe8721_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"33\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric coefficient of component 3 in process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-65d8d47d4329484c62443ecfb95a4a27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#44;&#32;&#102;&#105;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"39\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Fix costs of process I in \u20ac\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">1000<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-47ff26e562893bf9fe46d12df9a85bac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#44;&#32;&#102;&#105;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"44\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Fix costs of process II in \u20ac\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">1500<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-8425754ddb571d5a497ede40e20e6b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#44;&#32;&#102;&#105;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Fix costs of process III in \u20ac\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">3500<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-8bd3cac7b7c0eba82b4e2d21fc039c87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#44;&#32;&#118;&#97;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"41\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Variable costs of process I in \u20ac\/t<\/td><td class=\"has-text-align-left\" data-align=\"left\">1000<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-00859e5d6a2240adc5b57ab6a23c5282_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#44;&#32;&#118;&#97;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"47\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Variable costs of process II in \u20ac\/t<\/td><td class=\"has-text-align-left\" data-align=\"left\">1200<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5529d233991ee3941c1b910ea04b94d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#44;&#32;&#118;&#97;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"52\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Variable costs of process III in \u20ac\/t<\/td><td class=\"has-text-align-left\" data-align=\"left\">2000<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-4f53e2d3670c8d7a93fc1c97c85f1e3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#118;&#97;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"36\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Costs for component 1<\/td><td class=\"has-text-align-left\" data-align=\"left\">1800<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-2c00f90b9aa8b748fe89931b875e8aee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#118;&#97;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Costs for component 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">7000<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-e88eef09524dca7ab0da876429db11b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#118;&#97;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Selling price for component 3<\/td><td class=\"has-text-align-left\" data-align=\"left\">13000<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ec56d95c4b98b4654b91c271906106fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#49;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 1 in stream 1 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-8659ade4316a7544ca3282fb34fc6a12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#51;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 1 in stream 3 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">2.87<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-c9bb28c4dcb94c3d06820a4885160daf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#53;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 1 in stream 5 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.6<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5635cff1b9b3c4e3e4871d3433c1caff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#49;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 2 in stream 1 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-16c6b858e62b2ed96f0e30daa7b7a136_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#51;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 2 in stream 3 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-6a32d8e31cc93edc167e9830f0bec1e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#53;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 2 in stream 5 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">2<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-83b558675dd4880dd7070e39057e7fdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#49;&#44;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 3 in stream 1 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-8bf73791eea8780936e57fba34217f3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#51;&#44;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 3 in stream 3 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-fe9d1ddc5eff83dbf2195a5e0b6d9245_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#53;&#44;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Feed of component 3 in stream 5 in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ecafafd795dc5dc2038aa46f7d5b4348_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#50;&#44;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#109;&#97;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"63\" style=\"vertical-align: -8px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Maximum capacity of process I in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">4<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-06ec4252a6480e3b82ddcbf2c4a728bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#52;&#44;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#109;&#97;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"63\" style=\"vertical-align: -8px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Maximum capacity of process II in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">5<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-349776e91eda1d8957c61afc96a491c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#55;&#44;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#109;&#97;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"63\" style=\"vertical-align: -8px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Maximum capacity of process III in t\/h<\/td><td class=\"has-text-align-left\" data-align=\"left\">2<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-d43a11eac7cda5c8ef718ed32dd2a226_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"13\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion factor of process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-986742493fcdfd5fcd8de474807bfa56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"19\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion factor of process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.2<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-95b344d23e86051d7861eb8d3abbec2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion factor of process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.9<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-582510931040302a95a28c75bbcad009_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"14\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Binary decision variable for process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ee40f667c749b286d269c811cd940868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"20\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Binary decision variable for process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-729e5ed3efed705273b5aea483c0d8a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Binary decision variable for process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-9853456abd3977c798a303b561cd8a94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#50;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 1 in stream 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-033dfad79a496729a0f7b534339281ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#52;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 1 in stream 4<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.24<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-1fab306bef61358620b5e541a201f9ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#54;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 1 in stream 6<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.24<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-247efbca2137f6e6135a3526a9695583_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#55;&#44;&#99;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 1 in stream 7<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.24<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-6666fae5a5e443513ba2a00b01da2762_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#50;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 2 in stream 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-cf568603bab2698b8aa0fcf756e86ab9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#52;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 2 in stream 4<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.62<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-4c191936fcc91175bf0dc42d8311436c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#54;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 2 in stream 6<\/td><td class=\"has-text-align-left\" data-align=\"left\">2<\/td><td class=\"has-text-align-left\" data-align=\"left\">2.2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-1445a90e58ffb4ab04bc269c4206a7da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#55;&#44;&#99;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 2 in stream 7<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.22<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-41488209a626989354a722428b5ba1bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#50;&#44;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 3 in stream 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-3f9f3b2eb96b04de84b9dea8e008fe80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#52;&#44;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 3 in stream 4<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-65b6c8eabfecc3454feb512f8bc62a88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#54;&#44;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 3 in stream 6<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ec481b59f299e1d93718ac187cc34c57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#95;&#123;&#115;&#61;&#55;&#44;&#99;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -6px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Component flow of component 3 in stream 7<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.8<\/td><td class=\"has-text-align-left\" data-align=\"left\">2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-850f61e9dbafe507321352b867fa6abe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"36\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 1 in process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-b26fac04490dff5733240060d5d264c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 2 in process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-7cb82c64e82323d797a3eb7e26ed1fb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 3 in process I<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-133a85804afb9ae0a545b9b8c8fd4e2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"36\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 1 in process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">-1.62<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-f4a33272aecdef68c3da63594378949e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 2 in process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.62<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ebc35e089e1be296d0ec09ea81ff4829_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 3 in process II<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-78c80509a5947d7725d7595bd1098eaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#49;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"36\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 1 in process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-d54528052cd1f26d7632b9202e6f3b4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#50;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 2 in process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">-1.8<\/td><td class=\"has-text-align-left\" data-align=\"left\">-2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-79ba30e6224f34fc1325d9d01e9b4bbd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#95;&#123;&#99;&#61;&#51;&#125;&#94;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#73;&#73;&#73;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Conversion rate of component 3 in process III<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.8<\/td><td class=\"has-text-align-left\" data-align=\"left\">2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-f1bab0cd523067587582231ae6904381_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#105;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"30\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Dummy variable 1<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-6b40bfeb7eb890ecbe7e770b857a2d9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#105;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"31\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Dummy variable 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-b981e8796ec537002212d01015407c0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#105;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"31\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Dummy variable 3<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">-3.38<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-cf24d34e601f159d0864d7cd8c37da9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#95;&#123;&#105;&#61;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"31\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Dummy variable 4<\/td><td class=\"has-text-align-left\" data-align=\"left\">-0.2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-21f36758b04341c7980aa18b13ced720_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#80;&#104;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Objective function value<\/td><td class=\"has-text-align-left\" data-align=\"left\">-2300<\/td><td class=\"has-text-align-left\" data-align=\"left\">-5697.1<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 3: Initialization and results of the optimization.<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>This tutorial explains how a simple process synthesis problem can be set up and solved. This synthesis problem results in an mixed-integer nonlinear programming problem. Synthesis problem The synthesis problem contains two options (process I and II) to produce B from A. These processes vary in their fixed and variable costs. In addition, there is [&hellip;]<\/p>\n","protected":false},"author":252,"featured_media":0,"parent":5203,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5208","page","type-page","status-publish","czr-hentry"],"_links":{"self":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5208","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/users\/252"}],"replies":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5208"}],"version-history":[{"count":55,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5208\/revisions"}],"predecessor-version":[{"id":6167,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5208\/revisions\/6167"}],"up":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5203"}],"wp:attachment":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}