{"id":4892,"date":"2025-05-17T10:02:21","date_gmt":"2025-05-17T04:32:21","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=4892"},"modified":"2025-07-22T12:44:25","modified_gmt":"2025-07-22T07:14:25","slug":"linear-programming","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/me\/industrial-engineering\/linear-programming","title":{"rendered":"Linear Programming"},"content":{"rendered":"<p>It is a mathematical technique for determining optimal allocation of resources.<\/p>\n<ul>\n<li><strong>Objective Function:<\/strong> Clearly identifiable and measurable in quantity e.g. maximization of profit.<\/li>\n<li><strong>Constraints:<\/strong> These are limited resources with in which we have to make the objective function maximum<\/li>\n<\/ul>\n<p style=\"text-align: center;\">z = c1x1 + c2x2 + &#8230;<\/p>\n<p style=\"text-align: center;\">a11 x1 + a12 x2 + &#8230; \u2265 b1<\/p>\n<p style=\"text-align: center;\">Cj = profit coefficient<br \/>\nbi = resource value<br \/>\naij = technological coefficient<br \/>\nxj = variable<\/p>\n<ul>\n<li><strong> Special Cases:<\/strong> Linear programming problems can be solved by\u2013 Graphical method<\/li>\n<li><strong>Infinite Solution:<\/strong> Objective function slope equals to one of the constrain which forms the boundary.<\/li>\n<li style=\"text-align: justify;\"><strong>No Solution:<\/strong> It is not possible to find feasible solution which satisfy all the constrain.<\/li>\n<li style=\"text-align: justify;\"><strong>Unbounded Solution:<\/strong> The greatest value of objective function occurs at infinite and it simply means the common feasible region is not bounded by limit on constrain.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/me\/industrial-engineering\/xyz-analysis\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/me\/economic-order-quantity-eoq\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/me\/industrial-engineering\/sde-analysis\/\" target=\"_blank\" rel=\"noopener\"><strong>What is Industrial Engineering?<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>It is a mathematical technique for determining optimal allocation of resources. Objective Function: Clearly identifiable and measurable in quantity e.g.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1505,10],"tags":[1541,1542],"class_list":["post-4892","post","type-post","status-publish","format-standard","hentry","category-industrial-engineering","category-me","tag-infinite-solution","tag-unbounded-solution"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/4892","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=4892"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/4892\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=4892"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=4892"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=4892"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}