The NCERT solutions for the questions given in Chapter 12, Linear Programming , of the Class 12 NCERT textbooks are available here. We can say that linear programming is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. In this chapter students learn about Linear Programming in detail. Solving all the questions from this chapter of the NCERT book of class 12 maths, repeatedly, will help the students in understanding the methods of solving the questions.

The class 12 NCERT solutions of the chapter Linear Programming are very easy to understand as the subject experts at BYJUâ€™S ensure that the solutions are given in simplest form. These solutions cover all the exercise questions included in the book and are in accordance with the latest CBSE guidelines. Here, the PDF of the NCERT Solutions class 12 maths of chapter 12 is available which can be downloaded and referred in online mode. Students can also avail these NCERT solutions and download it for free.

### Download PDF of NCERT Solutions for Class 12 Maths Chapter 12- Linear Programming

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## NCERT Solutions for Class 12 Maths Chapter 12- Linear Programming

The major concepts of Maths covered in Chapter 12- Linear Programming of NCERT Solutions for Class 12 includes:

12.1 Introduction

12.2 Linear Programming Problem and its Mathematical Formulation

12.2.1 Mathematical formulation of the problem

12.2.2 Graphical method of solving linear programming problems

12.3 Different Types of Linear Programming Problems

12.3.1 Manufacturing problems

12.3.2 Diet problems

12.3.3 Transportation problems

Exercise 12.1 Solutions 10 Questions

Exercise 12.2 Solutions 11 Questions

Miscellaneous Exercise On Chapter 12 Solutions 10 Questions

## NCERT Solutions for Class 12 Maths Chapter 12 â€“ Linear Programming

The chapter Linear Programming itself makes up to a whole unit, Unit Five â€“ Linear Programming, that carries 5 marks of the total 80 marks. There are 2 exercises along with a miscellaneous exercise in this chapter to help students understand the concepts related to Linear Programming thoroughly. Some of the topics discussed in Chapter 12 of NCERT Solutions for Class 12 Maths are as follows:

- A linear programming problem is one that is concerned with finding the optimal value (maximum or minimum) of a linear function of several variables (called objective function) subject to the conditions that the variables are non-negative and satisfy a set of linear inequalities (called linear constraints). Variables are sometimes called decision variables and are non-negative.
- A few important linear programming problems are:
(i) Diet problems

(ii) Manufacturing problems

(iii) Transportation problems

- The common region determined by all the constraints including the non-negative constraints x â‰¥ 0, y â‰¥ 0 of a linear programming problem is called the feasible region (or solution region) for the problem.
- Points within and on the boundary of the feasible region represent feasible solutions of the constraints.
- Any point outside the feasible region is an infeasible solution.
- Any point in the feasible region that gives the optimal value (maximum or minimum) of the objective function is called an optimal solution.

- The Theorems that are fundamental in solving linear programming problems.
- If the feasible region is unbounded, then a maximum or a minimum may not exist. However, if it exists, it must occur at a corner point of R.
- Corner point method for solving a linear programming problem.
- If two corner points of the feasible region are both optimal solutions of the same type, i.e., both produce the same maximum or minimum, then any point on the line segment joining these two points is also an optimal solution of the same type

### Key Features of NCERT Solutions for Class 12 Maths Chapter 12- Linear Programming

Studying the Linear Programming of Class 12 enables the students to understand the following:

Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).