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

Our methodical and logical NCERT Solutions for Class 12 Maths Chapter 12- Linear Programming follow the latest class 12 maths syllabus. This chapter comprises a variety of important linear programming related topics such as feasible region, optimal solution, theorems of linear programming, corner point method of solving linear programming problems, graphical method of solving linear programming problems, and Isom-profit or iso-cost method of solving a linear programming problem. Our NCERT Solutions comprehensively cover all these topics. They contain all solved examples, and detailed explanations to help you gain an in-depth understanding of the chapter.

CBSE NCERT Class 12 Maths Chapter 12 comprises 2 exercises and 1 miscellaneous exercise. The questions from these exercises cover all question types and concepts from the chapter giving you ample practice to strengthen your conceptual base. Our NCERT Solutions contain step by step solutions of all questions of all the exercises. All questions have been solved using the best methods of solving the problems.

Our NCERT Solutions have been drafted in a manner to clear all your doubts quickly and help you learn at your convenience from anywhere and anytime. Our smart study techniques and Maths shortcuts give your exam preparation an edge over others. They make learning a less time consuming and effortless activity. They are just what you need to excel in your class 12 board exams.

## NCERT CBSE Class 12 Maths Chapter 12

The NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming cover all topics and sub-topics covered in this chapter. Some of them have been discussed below.

**Feasible region**

In this section, you will get to know about the meaning of feasible regions. A solution region or feasible region is defined as the common region that is represented by all the boundaries, including the non-negative boundaries x ≥ 0, y ≥ 0.

This chapter also teaches you about feasible choice, infeasible choice, and infeasible solution.

**Optimal solution**

Under this topic of CBSE NCERT Class 12 Maths Chapter 12, you will get to know about some fundamental theorems like the optimal solution of an objective function. The optical solution in an objective function of any point in the feasible region gives the optimal maximum value or the optimal minimum value.

**Theorems of linear programming**

In this section, of NCERT Class 12 Maths Chapter 12, you will learn about crucial theorems that will help in solving problems related to linear programming. The theorems are elaborated with examples so that you do not face any difficulties in learning. Following are the two theorems covered in this section on NCERT Class 12 Maths Chapter 12.

**Theorem 1**

Let R be the feasible region (convex polygon) for a linear programming problem.

Let Z = ax + by be the objective function.

When Z has an optimal value (Maximum or minimum) where the variables x and y are subject to boundaries described by linear inequalities, this optimal value must occur at a corner point (vertex) of the feasible region.

**Theorem 2**

Let R be the feasible region (convex polygon) for a linear programming problem.

Let Z = ax + by be the objective function.

If R is constrained, then the objective function Z has both minima, and maximum value of R and each of these occurs at a corner point (vertex) of R

Class 12 Maths Linear Programming chapter teaches you about the corner point method of solving linear programming problems within a feasible region. It also teaches you the graphical method to solve linear programming problems and Isom-profit or iso-cost method of solving a linear programming problem.

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

This chapter comprises 2 exercises and 1 miscellaneous exercise. Our NCERT Solution for Class 12 Maths Chapter 12 Linear Programming answers all questions in a step by step manner to help you understand easily. The exercises have been discussed below.

**Exercise 12.1 & 12.2**

Exercise 12.1 comprises 10 questions and exercise 12.2 consists of a total of 11 questions. The questions from these exercises cover various topics of the chapter. The topics covered include the feasible region, optimal solution, theorems of linear programming, linear programming and its applications, the graphical method to solve and linear programming, and corner point method of solving linear programming. They give you ample practice to become thorough with the concepts of the chapter.

The miscellaneous exercises of this chapter consist of a total of 11 questions. The numerical problems of this exercise are from all the topics that cover under this chapter.

### Benefits of NCERT Class 12 Maths Chapter 12 Solutions

There are a plethora of benefits associated with refereeing and learning from our NCERT Solution for Class 12 Maths Chapter 12 Linear Programming. Some of them have been given below.

- They are easy to understand, absolutely accurate, and precise solutions that facilitate fast and effective learning.
- They have been devised in a manner to cover all possible question types that are important from the board exam point of view.
- They offer you extensive practice and productive revision sessions that help you score high marks in your exams.
- They cover all topics and subtopics of the chapter to ensure you don’t miss out on anything.
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