# NCERT Exemplar Class 12 Maths Chapter 12 Solutions: Linear Programming

NCERT Exemplar Class 12 Maths Solutions Chapter 12 ‘Linear Programming’ are designed to make you well versed in this topic. This chapter makes use of the previous problem of ‘linear inequalities’ that you already covered in NCERT Exemplar Class 12 Maths. As we already know that linear inequalities can be solved in many ways; hence using that concept, we will move forward in this chapter. Here you will mainly deal with the optimization problem in linear programming.

In this chapter, there are 45 exemplar problems divided into various exercises. These questions are framed as short-answer type, long-answer type, multiple-choice questions (MCQs), true-false questions, and fill in blanks type questions. These questions are set up so that you can assemble essential ideas required to tackle similar problems in the CBSE class 12 exams. It is one of the crucial topics from the perspective of competitive exams like JEE Mains and JEE Advance.

Instasolv’s NCERT Exemplar problems with solutions for class 12 Maths Chapter 12 are made after complete research of the latest CBSE Class 12 Maths syllabus for linear programming. This chapter has high weightage in CBSE Class 12 board exams. You will encounter the mathematical formulation of the problem, the graphical method to solve such questions, and various types of linear programming problems.

## Important Topics for NCERT Exemplar Class 12 Maths Solutions Chapter 12 – Linear Programming

In NCERT Exemplar Class 12 Maths problems and solutions for chapter 12, you need to understand the basic concepts of a linear programming problem and its mathematical formulation. There are several types of mathematical problems discussed in this chapter, namely: Manufacturing problem, Transportation problem, diet problems.

**Optimization Problem:** Any problem that wants to maximize or minimize a function is called an optimization problem. An optimization problem can involve maximization of profit, production or minimization of cost, from available resources, etc.

**Linear programming problem:** It deals with the optimization of a linear function of two variables, which are known as the objective function. It is subjected to the conditions that the variables are non-negative and satisfy a set of linear inequalities. It is a special type of optimization problem.

**Theorem 1:** Let R be the feasible region for an LPP and let Z = ax + by be the objective function. When Z has an optimal value, where x and y are subject to constraints described by linear inequalities, this optimal value must occur at a corner point of the feasible region.

**Theorem 2:** Let R be the feasible region for an LPP and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R, and each of these occurs at a corner point of R.

**Multiple optimal points:** If the two corner points of some feasible region are optimal solutions of a similar type, i.e., both produce the same maximum or minimum, then any given point on that line segment joining these two points will also be an optimal solution of the same type.

These points are clarified with standard language and models. The activity is made to clear ideas all the more completely and will help you in all the competitive exams to follow. In any case, for that, you have to experience each solution of Exemplar problems as given by Instasolv.

### Exercise Discussion of NCERT Exemplar Class 12 Maths Solutions Chapter 12 – Linear Programming

- The first 15 exemplar problems are short answer types. They test your necessary skills and formula applications on topics like solving, finding the optimum solution and calculating the maximum and minimum value.
- The next 10 questions from 16-25 are long answer types, which are based mostly on numerical problems to find the mathematical solution of linear programming
- MCQs are given the main emphasis in this exercise due to the high weightage in competitive exams. Questions 26-34 are MCQs which are based on finding the vertex value and test your theoretical knowledge.
- Questions 35-41 are fill-in the blanks problems, and 42-45 are true-false questions based on all the topics of the chapter on topics like the objective function of LPP, the feasible region of linear inequalities, the maximum and minimum value of the objective function.

## Why Use NCERT Exemplar Class 12 Maths Solutions Chapter 12 by Instasolv?

- NCERT Exemplar Class 12 Maths Problems and Solutions for Chapter 12 is a very authentic source of learning. Class 12 is always a pressure, but our Exemplar problems with solutions will help you a lot.
- We have provided all the solved exemplar problems for chapter 12 online without any cost. It is always suggested by study experts to follow these solutions stepwise to get a clear understanding of the concepts.