{"id":60458,"date":"2022-01-29T23:31:01","date_gmt":"2022-01-29T18:01:01","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=60458"},"modified":"2024-01-18T17:04:37","modified_gmt":"2024-01-18T11:34:37","slug":"ncert-exemplar-solutions-for-class-12-maths-chapter-12-linear-programming","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-12-linear-programming\/","title":{"rendered":"NCERT Exemplar Solutions for Class 12 Maths Chapter 12 &#8211; Linear Programming"},"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\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-12-linear-programming\/#Beneath_are_the_theoretical_concepts_covered_in_Class_12_Maths_Chapter_12_Linear_Programming\" title=\"Beneath are the theoretical concepts covered in Class 12 Maths Chapter 12 Linear Programming: \">Beneath are the theoretical concepts covered in Class 12 Maths Chapter 12 Linear Programming: <\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-12-linear-programming\/#121_Introduction\" title=\"12.1 Introduction\">12.1 Introduction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-12-linear-programming\/#122_Linear_Programming_Problem_and_its_Mathematical_Formulation\" title=\"12.2 Linear Programming Problem and its Mathematical Formulation\">12.2 Linear Programming Problem and its Mathematical Formulation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-12-linear-programming\/#123_Different_Types_of_Linear_Programming_Problems\" title=\"12.3 Different Types of Linear Programming Problems\">12.3 Different Types of Linear Programming Problems<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-12-linear-programming\/#The_number_of_questions_available_in_the_exercise_of_NCERT_Exemplar_Solutions_for_Class_12_Maths_Chapter_12\" title=\"The number of questions available in the exercise of NCERT Exemplar Solutions for Class 12 Maths Chapter 12 :\">The number of questions available in the exercise of NCERT Exemplar Solutions for Class 12 Maths Chapter 12 :<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-12-linear-programming\/#A_few_points_on_NCERT_Class_12_Maths_Chapter_12_Linear_Programming\" title=\"A few points on NCERT Class 12 Maths Chapter 12 Linear Programming\">A few points on NCERT Class 12 Maths Chapter 12 Linear Programming<\/a><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-12-linear-programming\/#How_many_problems_are_there_in_each_exercise_of_the_NCERT_Exemplar_Solutions_for_Class_12_Maths_Chapter_12\" title=\"How many problems are there in each exercise of the NCERT Exemplar Solutions for Class 12 Maths Chapter 12?\">How many problems are there in each exercise of the NCERT Exemplar Solutions for Class 12 Maths Chapter 12?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-12-linear-programming\/#What_do_you_mean_by_linear_programming_in_Chapter_12_of_NCERT_Exemplar_Solutions_for_Class_12_Maths\" title=\"What do you mean by linear programming in Chapter 12 of NCERT Exemplar Solutions for Class 12 Maths?\">What do you mean by linear programming in Chapter 12 of NCERT Exemplar Solutions for Class 12 Maths?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-12-linear-programming\/#Where_can_I_get_NCERT_Exemplar_Solutions_for_Class_12_Maths_Chapter_12_online\" title=\"Where can I get NCERT Exemplar Solutions for Class 12 Maths Chapter 12 online?\">Where can I get NCERT Exemplar Solutions for Class 12 Maths Chapter 12 online?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-12-linear-programming\/#Why_Opt_for_Infinity_Learn\" title=\"Why Opt for Infinity Learn?\">Why Opt for Infinity Learn?<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">Subject specialists have created NCERT Exemplar Solutions for Class 12 Maths Chapter 12 Linear Programming, which includes thorough solutions for reference. All of the questions from the textbook&#8217;s exercises are answered here. Students can use these answers to help them prepare for their exams. The NCERT Exemplar Solutions for Class 12 provide useful solutions for improving conceptual knowledge and preparing for <strong><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/jee\" target=\"_blank\" rel=\"noopener\">JEE<\/a><\/span><\/strong>.<\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving<strong> <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/\" target=\"_blank\" rel=\"noopener\">NCERT Exemplar Solutions for Class 12<\/a><\/span><\/strong>. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 12 pupils perform well in upcoming competitive exams.<\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.<\/span><\/p>\n<h2><span style=\"font-size: 14pt; color: #0000ff;\">Beneath are the theoretical concepts covered in Class 12 Maths Chapter 12 Linear Programming:<span style=\"font-weight: 400;\"> <\/span><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"121_Introduction\"><\/span><span style=\"font-size: 12pt;\"><b>12.1 Introduction<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">This section summarises the preceding grades&#8217; discussions of linear equations, linear inequalities, and linear inequalities applications. It uses an example to illustrate the concept of optimization problems and a subset of optimization problems known as linear programming problems. The maximization of profit while lowering the cost of a production unit is an excellent example of optimization.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"122_Linear_Programming_Problem_and_its_Mathematical_Formulation\"><\/span><span style=\"font-size: 12pt;\"><b>12.2 Linear Programming Problem and its Mathematical Formulation<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">This section contains an example of a furniture trader who is attempting to optimize revenues by experimenting with various chair and table combinations.<\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">12.2.1 Mathematical formulation of the problem<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">The formulation of the above-mentioned mathematical issue is further explained in this part. The non-negative restrictions, objective function, and decision variables are all defined in this document.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">An objective function can be used to define the optimal value of a linear function.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">Finding the optimal value [maximum or minimum] of a linear function of variables subject to particular conditions and satisfying a set of linear constraints is a linear programming issue.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">Decision variables are variables that are involved in the objective function.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">The variables are restricted by the constraints.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">12.2.2 Graphical method of solving linear programming problems<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">The definition of the feasible region, feasible and infeasible solutions, optimal solutions, and bounded and unbounded feasible solution regions are all covered in this section. It gives a quick overview of the Corner Point Method, which is used to solve linear programming issues and includes examples.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">The feasible region is defined as the region obtained by the restrictions [including non-negative constraints].<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">Possible solutions are the points that fall within the practicable zone.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">Infeasible solutions are points outside of the feasible zone.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">An optimal solution is a point in the feasible zone that offers the optimal value of the objective function.<\/span><\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"123_Different_Types_of_Linear_Programming_Problems\"><\/span><span style=\"font-size: 12pt;\"><b>12.3 Different Types of Linear Programming Problems<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">Different types of linear programming problems are discussed in this section.<\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">12.3.1 Manufacturing problems<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">These issues can be encountered in the manufacturing industry in order to maximize earnings while optimizing production. Profits can be determined by the number of employees, working hours, resources required, the market value of the product, demand for the product, supply of the product, and so on.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">12.3.2 Diet problems<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">Such issues entail optimizing the number of different types of foods consumed in order for the body to acquire the nutrients it requires. A diet problem&#8217;s aim will be to choose foods that provide the essential nutrition at a lower cost.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">12.3.3 Transportation problems<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">These issues concern the efficient delivery of manufactured items to various locations at the lowest possible cost. The analysis of transportation costs is very important for large companies because it caters to a wide area.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-size: 12pt;\"><span style=\"font-weight: 400;\">Students can utilize the Infinity Learn <\/span>NCERT Exemplar Solutions for Class 12 Maths Chapter 12<span style=\"font-weight: 400;\"> for learning any kind of complex topic.<\/span><\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"The_number_of_questions_available_in_the_exercise_of_NCERT_Exemplar_Solutions_for_Class_12_Maths_Chapter_12\"><\/span><span style=\"font-weight: 400; font-size: 12pt;\">The number of questions available in the exercise of NCERT Exemplar Solutions for Class 12 Maths Chapter 12 :<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li><span style=\"font-size: 12pt;\"><span style=\"font-weight: 400;\">Exercise 12.1 Solutions<\/span><span style=\"font-weight: 400;\"> \u2013 10 Questions<\/span><\/span><\/li>\n<li><span style=\"font-weight: 400; font-size: 12pt;\">Exercise 12.2 Solutions \u2013 11 Questions<\/span><\/li>\n<li><span style=\"font-weight: 400; font-size: 12pt;\">Miscellaneous Exercise On Chapter 12 Solutions \u2013 10 Questions<\/span><\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"A_few_points_on_NCERT_Class_12_Maths_Chapter_12_Linear_Programming\"><\/span><strong><span style=\"font-size: 12pt;\">A few points on NCERT Class 12 Maths Chapter 12 Linear Programming<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">The chapter Linear Programming is divided into five units, each of which is worth five points out of a possible eighty. This chapter includes two exercises as well as a miscellaneous activity to help students fully comprehend the fundamentals of linear programming. The following are some of the topics covered in Chapter 12 of NCERT Exemplar Solutions for Class 12 Maths:<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400; font-size: 12pt;\"> A linear programming issue is one in which the goal is to determine the best value (maximum or minimum) of a linear function of numerous variables (called the objective function), given that the variables are non-negative and the variables satisfy a set of linear inequalities (called linear constraints). Decision variables are non-negative variables that are sometimes referred to as decision variables.<\/span><\/li>\n<li><span style=\"font-weight: 400; font-size: 12pt;\"> The important linear programming problems are listed below:<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">Diet problems<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">Manufacturing problems<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">Transportation problems<\/span><\/li>\n<\/ul>\n<ol start=\"3\">\n<li><span style=\"font-weight: 400; font-size: 12pt;\"> The viable region (or solution region) of a linear programming problem is the common region given by all the constraints, including the non-negative constraints x 0, y 0.<\/span><\/li>\n<li><span style=\"font-weight: 400; font-size: 12pt;\"> Possible solutions to the limitations are represented by points within and on the boundary of the viable zone.<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">A solution that is outside the feasible zone is infeasible.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">An optimal solution is a point in the feasible zone that gives the objective function&#8217;s optimal value (maximum or minimum).<\/span><\/li>\n<\/ul>\n<ol start=\"5\">\n<li><span style=\"font-weight: 400; font-size: 12pt;\"> If the viable zone is unbounded, there may be no maximum or minimum. If it does exist, it must occur at an R corner point.<\/span><\/li>\n<li><span style=\"font-weight: 400; font-size: 12pt;\"> When addressing a linear programming issue, the corner point approach is applied.<\/span><\/li>\n<li><span style=\"font-weight: 400; font-size: 12pt;\"> If two feasible region corner points are both optimal solutions of the same kind, i.e., they yield the same maximum or minimum, then every point on the line segment connecting them is likewise an optimal solution of the same type.<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">Students can learn about the following topics by studying Linear Programming in Class 12 with NCERT Exemplar Solutions: introduction, related terminologies such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, and more. viable and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions, the graphical technique of solution for problems in two variables (up to three non-trivial constraints). Furthermore, the NCERT Exemplar Solutions boosts pupils&#8217; confidence when it comes to taking future tests.<\/span><\/p>\n<p><strong><span style=\"font-size: 14pt; color: #0000ff;\">Frequently Asked Questions<\/span><\/strong><\/p>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"How_many_problems_are_there_in_each_exercise_of_the_NCERT_Exemplar_Solutions_for_Class_12_Maths_Chapter_12\"><\/span>How many problems are there in each exercise of the NCERT Exemplar Solutions for Class 12 Maths Chapter 12?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThree problems are included in Chapter 12 of the NCERT Exemplar Solutions for Class 12 Maths. Exercise 12.1 contains 10 questions, Exercise 12.2 contains 11 questions, and the miscellaneous exercise contains 10 questions that span all of the concepts in this chapter. Every problem is addressed with the utmost care in order to deliver accurate solutions to the students in accordance with CBSE norms.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"What_do_you_mean_by_linear_programming_in_Chapter_12_of_NCERT_Exemplar_Solutions_for_Class_12_Maths\"><\/span>What do you mean by linear programming in Chapter 12 of NCERT Exemplar Solutions for Class 12 Maths?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tLinear programming is a mathematical concept in which mathematical functions are constrained and then minimized or maximized as a result. This chapter's objective functions and constraints are all totally linear. The minimum and maximum values of the linear functions are shown on the xy coordinate for further deductions. The basic goal of linear programming is to improve mathematical functions that are constrained by linear constraints.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"Where_can_I_get_NCERT_Exemplar_Solutions_for_Class_12_Maths_Chapter_12_online\"><\/span>Where can I get NCERT Exemplar Solutions for Class 12 Maths Chapter 12 online?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tINFINITY LEARN has the NCERT Exemplar Solutions for Class 12 Maths Chapter 12 available for download. Subject specialists curate the solutions to all of the problems so that students have the best reference material to rely on. You can download chapter-by-chapter or exercise-by-exercise solutions to acquire a better understanding of the problem-solving approaches used to solve textbook issues.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"Why_Opt_for_Infinity_Learn\"><\/span>Why Opt for Infinity Learn?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tIn this chapter Infinity Learn provides videos, notes, NCERT textbook solutions, other practice book solutions and assignments that help you learn the concepts and to memorise the concepts for entrance exams and board exams. Most important, Infinity learn provide instant doubt support by subject experts.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How many problems are there in each exercise of the NCERT Exemplar Solutions for Class 12 Maths Chapter 12?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Three problems are included in Chapter 12 of the NCERT Exemplar Solutions for Class 12 Maths. Exercise 12.1 contains 10 questions, Exercise 12.2 contains 11 questions, and the miscellaneous exercise contains 10 questions that span all of the concepts in this chapter. Every problem is addressed with the utmost care in order to deliver accurate solutions to the students in accordance with CBSE norms.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What do you mean by linear programming in Chapter 12 of NCERT Exemplar Solutions for Class 12 Maths?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Linear programming is a mathematical concept in which mathematical functions are constrained and then minimized or maximized as a result. This chapter's objective functions and constraints are all totally linear. The minimum and maximum values of the linear functions are shown on the xy coordinate for further deductions. The basic goal of linear programming is to improve mathematical functions that are constrained by linear constraints.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Where can I get NCERT Exemplar Solutions for Class 12 Maths Chapter 12 online?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"INFINITY LEARN has the NCERT Exemplar Solutions for Class 12 Maths Chapter 12 available for download. Subject specialists curate the solutions to all of the problems so that students have the best reference material to rely on. You can download chapter-by-chapter or exercise-by-exercise solutions to acquire a better understanding of the problem-solving approaches used to solve textbook issues.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Why Opt for Infinity Learn?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"In this chapter Infinity Learn provides videos, notes, NCERT textbook solutions, other practice book solutions and assignments that help you learn the concepts and to memorise the concepts for entrance exams and board exams. Most important, Infinity learn provide instant doubt support by subject experts.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Subject specialists have created NCERT Exemplar Solutions for Class 12 Maths Chapter 12 Linear Programming, which includes thorough solutions for [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"NCERT Exemplar Solutions for Class 12 Maths Chapter 12","_yoast_wpseo_title":"NCERT Solutions for Class 12 Maths Chapter 12 - Linear Programming","_yoast_wpseo_metadesc":"Subject specialists have created NCERT Exemplar Solutions for Class 12 Maths Chapter 12 Linear Programming, which includes solutions.","custom_permalink":"study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-12-linear-programming\/"},"categories":[106,109,105],"tags":[7361,7362,7363],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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