Every linear programming problem involves optimizing a<\/p>\n\n\n\n
q,<\/p>\n\n\n\n
linear function subject to several non-linear constraints.<\/p>\n\n\n\n
non-linear function subject to several linear constraints.<\/p>\n\n\n\n
linear regression model subject to several linear constraints.<\/p>\n\n\n\n
linear function subject to several linear constraints.<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n Correct Answer:<\/strong> Linear programming (LP) is a mathematical technique used to determine the best possible outcome (such as maximum profit or minimum cost) in a mathematical model. The defining characteristics of a linear programming problem are:<\/p>\n\n\n\n Linear programming problems always involve a linear objective function<\/strong> and linear constraints<\/strong>. The power of LP lies in its ability to find optimal solutions efficiently under these conditions using algorithms like the Simplex method<\/strong> or graphical methods<\/strong> for two-variable problems.<\/p>\n","protected":false},"excerpt":{"rendered":" Every linear programming problem involves optimizing a q, linear function subject to several non-linear constraints. non-linear function subject to several linear constraints. linear regression model subject to several linear constraints. linear function subject to several linear constraints. The Correct Answer and Explanation is: Correct Answer:Linear function subject to several linear constraints. Explanation: Linear programming (LP) […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-215167","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/215167","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=215167"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/215167\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=215167"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=215167"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=215167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Linear function subject to several linear constraints.<\/strong><\/p>\n\n\n\n
\n\n\n\nExplanation:<\/strong><\/h3>\n\n\n\n
\n
This is the function that needs to be optimized\u2014either maximized<\/strong> (e.g., profits) or minimized<\/strong> (e.g., costs). It is linear, meaning it involves variables raised only to the first power, with no products or nonlinear operations like squares or square roots.
Example:
Z=5x+3yZ = 5x + 3y, where ZZ is the objective function to be maximized or minimized, and xx and yy are decision variables.<\/li>\n\n\n\n
These are the restrictions or limitations on the decision variables, and they also must be linear. Constraints are expressed as linear equations or inequalities.
Example:
2x+y\u2264102x + y \\leq 10
x\u22650,y\u22650x \\geq 0, y \\geq 0 (Non-negativity constraints)<\/li>\n<\/ol>\n\n\n\n
\n\n\n\nWhy the Other Options Are Incorrect:<\/strong><\/h3>\n\n\n\n
\n
This describes a non-linear programming<\/strong> problem, not linear programming.<\/li>\n\n\n\n
This also falls under non-linear programming<\/strong>, because the objective function is not linear.<\/li>\n\n\n\n
Linear regression is a statistical technique for predicting the value of a variable. It is not an optimization method in the same context as linear programming.<\/li>\n<\/ul>\n\n\n\n
\n\n\n\nConclusion:<\/strong><\/h3>\n\n\n\n