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NCERT Books Free Download for Class 12 Maths Chapter-12 Linear Programming

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Last updated date: 23rd Jul 2024
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NCERT Books for Class 12 Maths Chapter-12 Linear Programming Free PDF Download

In order to tackle real-life situations, NCERT books for class 12 Math chapter 12 Linear Programming uses systems of linear inequalities/equations. In previous classes, students learned about several systems of linear equations and how to use them to solve everyday issues. Students were also taught about linear inequalities and systems of linear inequalities in two variables, as well as how to solve them using graphical methods.


Chapter 12 of the NCERT book for Class 12 Mathematics is an easy yet crucial chapter with a wide range of industrial applications in Finance, Statistics, Mathematics, Economics, and other fields. There are various ways to tackle linear programming issues, but this topic concentrates on the graphical approach, which is the simplest. 


When children are addressing such problems, the most important thing they must remember is that the mathematical formulation must be completed correctly after reading the problem in total. It's quite simple to get the final result once they've deduced the necessary equations.

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Chapter 12 of the NCERT book for Class 12 Mathematics: A Few Points

The chapter Linear Programming is divided into five units.The following are some of the topics covered in Chapter 12 of NCERT Solutions for Class 12 Math:

  • 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. The following are some of the most important linear programming problems:

    • Dietary issues

    • Problems with manufacturing

    • Problems with transportation

  • The viable region (or solution domain) of a linear programming problem is the common region given by all the constraints, including the non-negative constraints.

  • Possible solutions to the restrictions are represented as points within and on the boundary of the feasible zone.

  • A solution that is outside the feasible zone is infeasible.

  • An optimal solution is a point in the feasible zone that gives the objective function's optimal value (maximum or minimum).

  • A maximum or minimum may not exist if the feasible region is boundless. If it does exist, it must occur at a R corner point.

  • When addressing a linear programming issue, the corner point approach is applied.

  • 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.

FAQs on NCERT Books Free Download for Class 12 Maths Chapter-12 Linear Programming

1. In Chapter 12 of NCERT Solutions for Class 12 Math, what do you mean by linear programming? Where can I find Chapter 12 of the NCERT math book for Class 12  online?

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.


On Vedantu, you can get the NCERT Solutions for Class 12 Math Chapter 12 for free. Subject specialists curate the solutions to all of the problems so that students have the best reference material to rely on.

2. Why is Chapter 12 of the NCERT math book for Class 12 important?

For students preparing for boards and competitive exams, Chapter 12 of the NCERT book for Class 12 mathematics is essential. They provide a step-by-step approach for solving all of the sums as well as a variety of tips and tricks for quickly cross-checking the final answer. In addition, the book teaches readers how to memorize formulas and concepts more quickly.

3. Why should I practise  Chapter 12 of Class 12 math NCERT book?

Practice is the way to go if a student wants to master a subject. Due to the uncertainty of the level of questions that may emerge, the 12th board may prove to be a difficult exam. As a result, in order to achieve the highest possible score, students must practise each question in Chapter 12 Linear Programming of the NCERT math book for Class 12 at least twice. They should also study over the question papers from previous exams to obtain a clear idea of the paper pattern.

4. How can CBSE students make the most of Chapter 12 of the NCERT book for Class 12 math?

The theory provided in each section of the NCERT textbook must first be reviewed by the students. After that, it's a good idea to go over all of the solved examples again. If students run into problems, they can go back to prior chapters and review the ideas. Finally, the NCERT Solutions Class 12 Math Chapter 12 can be utilized to cross-reference the answers and provide clarification on how to solve comparable problems.