{"id":155566,"date":"2022-03-26T00:47:17","date_gmt":"2022-03-25T19:17:17","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/optimization-in-mathematics-definition-problems-uses-and-solved-examples\/"},"modified":"2022-12-27T13:15:41","modified_gmt":"2022-12-27T07:45:41","slug":"optimization-in-mathematics-definition-problems-uses-and-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/optimization\/","title":{"rendered":"Optimization in Mathematics &#8211; Definition, Problems, Uses"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/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\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><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><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/optimization\/#What_is_Optimization\" title=\"What is Optimization?\">What is Optimization?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/optimization\/#Mathematical_Optimization_Problems\" title=\"Mathematical Optimization Problems\">Mathematical Optimization Problems<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/optimization\/#Optimization_Problems\" title=\"Optimization Problems\">Optimization Problems<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/optimization\/#Why_use_Mathematical_Optimization\" title=\"Why use Mathematical  Optimization?\">Why use Mathematical  Optimization?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/optimization\/#Mathematical_Optimization_Problems_in_business\" title=\"Mathematical Optimization Problems in business\">Mathematical Optimization Problems in business<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Optimization\"><\/span>What is Optimization?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Optimization in Mathematics &#8211; Definition: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/optimization\/\">Optimization<\/a> is the process of making something as efficient or effective as possible. In business, this can mean making sure that resources are used in the most efficient way possible, or that a process is as effective as it can be. For example, a business might try to optimize its production process in order to make the most products with the fewest resources.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-155565 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/optimization-in-mathematics-definition-problems-uses-and-solved-examples.jpg\" alt=\"Optimization in Mathematics - Definition, Problems, Uses and Solved Examples\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/optimization-in-mathematics-definition-problems-uses-and-solved-examples.jpg?v=1648235834 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/optimization-in-mathematics-definition-problems-uses-and-solved-examples-300x212.jpg?v=1648235834 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Mathematical_Optimization_Problems\"><\/span>Mathematical Optimization Problems<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Mathematical optimization problems are mathematical problems that involve the determination of the best possible solution to a problem. The best possible solution is usually determined by finding the minimum or maximum value of a function. Mathematical optimization problems can be difficult to solve, and also often require the use of sophisticated mathematical techniques.<\/p>\n<ul>\n<li>The world of business has an interesting relation to mathematics. The modern business world is extremely competitive, and in order to succeed, a company must be able to optimize its resources to get the maximum possible output. This is where mathematical optimization comes in.<\/li>\n<li>There are many types of optimization problems that a company may face. For example, a company may need to find the least cost production method for a new product, or it may need to find the most efficient delivery route for its products. Whatever the problem, there is usually a mathematical solution that can help the company to optimize its resources and achieve its goals.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Optimization_Problems\"><\/span>Optimization Problems<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>One of the most common optimization problems is the knapsack problem. This is where a company needs to choose the most efficient combination of products to produce in order to meet customer demand. The knapsack problem can be solved using a variety of different methods, including linear programming and integer programming.<\/li>\n<li>Another common optimization problem is the traveling salesman problem. This is where a company needs to find the most efficient route for its salesmen to travel in order to sell its products. The traveling salesman problem can solved using a variety of different methods, including the branch and bound method and the dynamic programming method.<\/li>\n<li>There are many other types of optimization problems that a company may face. However, these are two of the most common. In order to solve these problems, a company must first understand the problem and then use the appropriate mathematical methods to solve it.<\/li>\n<\/ul>\n<h2>Why use Mathematical  Optimization?<\/h2>\n<p>Mathematical optimization a technique used to find the best possible solution to a problem. It can used to find most efficient path for a travelling salesman. Therefore the best place to put a wind turbine, or the lowest-cost way to meet a set of constraints.<\/p>\n<p>The most common use of mathematical optimization is in business and economics, where it used to find the best way to allocate resources. However, it can used in any field where a decision needs to made under constraints.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Mathematical_Optimization_Problems_in_business\"><\/span>Mathematical Optimization Problems in business<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>Production planning, scheduling, and also sequencing<\/li>\n<li>Resource allocation<\/li>\n<li>Network design<\/li>\n<li>Linear programming<\/li>\n<li>Nonlinear programming<\/li>\n<li>Integer programming<\/li>\n<li>Dynamic programming<\/li>\n<li>Goal programming<\/li>\n<li>Queuing theory<\/li>\n<li>also Markov chains<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>What is Optimization? Optimization in Mathematics &#8211; Definition: Optimization is the process of making something as efficient or effective as [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Optimization in Mathematics - Definition","_yoast_wpseo_title":"%%title%% %%page%%","_yoast_wpseo_metadesc":"Optimization in Mathematics - Definition: Learn about Optimization topic in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/optimization\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Optimization in Mathematics - Definition, Problems, Uses<\/title>\n<meta name=\"description\" content=\"Optimization in Mathematics - Definition: Learn about Optimization topic in details explained by subject experts on infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/optimization\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Optimization in Mathematics - 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