{"id":206899,"date":"2025-04-17T07:22:24","date_gmt":"2025-04-17T07:22:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=206899"},"modified":"2025-04-17T07:22:27","modified_gmt":"2025-04-17T07:22:27","slug":"a-feasible-solution-to-an-lp-problem","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/17\/a-feasible-solution-to-an-lp-problem\/","title":{"rendered":"A feasible solution to an lp problem"},"content":{"rendered":"\n

A feasible solution to an lp problem
a) Must satisfy all of the problems constraints simultaneously
b) Need not satisfy all of the constraints, only some of them
c) Must be a corner point of the feasible region
d) Must optimize the value of the objective function<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

Correct Answer: a) Must satisfy all of the problem’s constraints simultaneously<\/strong><\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

In Linear Programming (LP)<\/strong>, a feasible solution<\/em> refers to any solution that satisfies all the constraints<\/strong> of the problem, including both the equality\/inequality constraints<\/em> and the non-negativity constraints<\/em> (if applicable).<\/p>\n\n\n\n

Let\u2019s break this down:<\/p>\n\n\n\n

1. Feasible Region<\/strong><\/h4>\n\n\n\n

An LP problem is defined by:<\/p>\n\n\n\n

    \n
  • An objective function<\/strong> (to be maximized or minimized),<\/li>\n\n\n\n
  • A set of constraints<\/strong> (usually linear inequalities or equalities).<\/li>\n<\/ul>\n\n\n\n

    The feasible region<\/strong> is the set of all points (combinations of variable values) that satisfy all<\/strong> these constraints simultaneously. A feasible solution is any point within this region.<\/p>\n\n\n\n

    2. Why Option (a) is Correct<\/strong><\/h4>\n\n\n\n

    For a solution to be feasible<\/em>, it must:<\/p>\n\n\n\n

      \n
    • Not violate any constraint,<\/li>\n\n\n\n
    • Lie within the feasible region.<\/li>\n<\/ul>\n\n\n\n

      If a point fails to meet even one constraint, it lies outside the feasible region and is considered infeasible<\/em>.<\/p>\n\n\n\n

      3. Why the Other Options are Incorrect<\/strong><\/h4>\n\n\n\n
        \n
      • (b)<\/strong>: Saying it “need not satisfy all of the constraints” contradicts the definition of feasibility. Violating any constraint makes the solution infeasible.<\/li>\n\n\n\n
      • (c)<\/strong>: While optimal solutions<\/strong> often occur at corner points (extreme points)<\/strong> of the feasible region (in linear problems), not all feasible solutions are corner points. Feasible solutions can lie anywhere in the feasible region, including along the edges or in the interior.<\/li>\n\n\n\n
      • (d)<\/strong>: A feasible solution does not necessarily<\/strong> optimize the objective function. It’s simply a candidate. Among all feasible solutions, the one that gives the best value of the objective function is the optimal solution<\/em>.<\/li>\n<\/ul>\n\n\n\n

        Summary<\/h4>\n\n\n\n

        A feasible solution is any point that satisfies all constraints<\/em> of the LP problem. It\u2019s a basic requirement, not necessarily the best (optimal) solution. Finding a feasible solution is the first step before seeking optimality.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        A feasible solution to an lp problema) Must satisfy all of the problems constraints simultaneouslyb) Need not satisfy all of the constraints, only some of themc) Must be a corner point of the feasible regiond) Must optimize the value of the objective function The correct answer and explanation is : Correct Answer: a) Must satisfy […]<\/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-206899","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206899","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=206899"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206899\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=206899"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=206899"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=206899"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}