{"id":206906,"date":"2025-04-17T07:27:29","date_gmt":"2025-04-17T07:27:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=206906"},"modified":"2025-04-17T07:27:31","modified_gmt":"2025-04-17T07:27:31","slug":"while-plotting-constraints-on-a-graph-paper-terminal-points-on-both-the-axes-are-connected-by-straight-line-because","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/17\/while-plotting-constraints-on-a-graph-paper-terminal-points-on-both-the-axes-are-connected-by-straight-line-because\/","title":{"rendered":"While plotting constraints on a graph paper, terminal points on both the axes are connected by straight line because"},"content":{"rendered":"\n

While plotting constraints on a graph paper, terminal points on both the axes are connected by straight line because:
a) The Resources are limited in supply b) the objective function as a linear
function c) the constraints are linear equations or inequalities d) All of the above<\/p>\n\n\n\n

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

Correct Answer: d) All of the above<\/strong><\/p>\n\n\n\n

Explanation (Approx. 300 words):<\/h3>\n\n\n\n

In linear programming, constraints are typically plotted on a graph to visually represent the feasible region \u2014 the set of all possible solutions that satisfy the given conditions. When plotting these constraints, the terminal points (intercepts) on the X-axis and Y-axis are connected by a straight line. This practice is based on several foundational principles of linear programming:<\/p>\n\n\n\n

    \n
  1. Constraints are Linear Equations or Inequalities (Option c):<\/strong>
    Constraints in linear programming are expressed in the form of linear equations or inequalities (e.g., ( ax + by \\leq c )). The graph of a linear equation is always a straight line. Therefore, when two intercepts (such as when ( x = 0 ) and ( y = 0 )) are determined and plotted, connecting them with a straight line accurately represents the constraint.<\/li>\n\n\n\n
  2. The Objective Function is a Linear Function (Option b):<\/strong>
    Though this doesn\u2019t directly affect how the constraints are graphed, it plays a role in why the entire problem is linear. The linearity of the objective function ensures that the optimization (maximization or minimization) over a linear feasible region is meaningful and that the solution lies at the boundary or vertex of the feasible region \u2014 which is shaped by straight lines from linear constraints.<\/li>\n\n\n\n
  3. Resources are Limited in Supply (Option a):<\/strong>
    This is the practical reason behind the constraints themselves. In real-world applications, resources like labor, materials, or time are finite. These limitations are mathematically expressed as inequalities, leading to the creation of constraint lines on a graph.<\/li>\n<\/ol>\n\n\n\n

    Conclusion:<\/h3>\n\n\n\n

    All three options are interconnected and essential to understanding why terminal points are connected by a straight line when graphing constraints. Hence, Option d) All of the above<\/strong> is the most comprehensive and correct answer.<\/p>\n\n\n\n

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

    While plotting constraints on a graph paper, terminal points on both the axes are connected by straight line because:a) The Resources are limited in supply b) the objective function as a linearfunction c) the constraints are linear equations or inequalities d) All of the above The correct answer and explanation is : Correct Answer: d) […]<\/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-206906","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206906","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=206906"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206906\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=206906"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=206906"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=206906"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}