**CBSE NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming** – is designed and prepared by the best teachers across India. All the important topics under NCERT Solutions for Class 12 Maths Chapter 12 are covered in this page and each answer comes with a detailed explanation to help students understand concepts better. These NCERT solutions play a crucial role in your preparation for all exams conducted by the CBSE, including the JEE.

Chapter 12 Linear Programming NCERT Solutions covers multiple exercises. The answer to each question in every exercise is provided along with complete, step-wise solutions for your better understanding. This will prove to be most helpful to you in your home assignments as well as practice sessions. Read on to find out everything about CBSE NCERT Solutions for Class 12 Maths Chapter 12.

**NCERT Solutions for Class 12 Maths Chapter 12 PDF**

The topics and sub-topics included in the & Linear Programming chapter are the following:

12.1 | Introduction |

12.2 | Linear Programming Problem and its Mathematical Formulation |

12.3 | Different Types of Linear Programming Problems |

**NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming PDF **

Candidates can download the NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming PDF for free study in offline mode. All the solutions provided in this page are solved by top academic experts of Embibe in order to help students in their studies.

**DOWNLOAD Linear Programming NCERT SOLUTIONS PDF**

**NCERT Solutions For Class 12 Maths Chapter 12 – Linear Programming NCERT Solutions**

In earlier classes, we have discussed systems of linear equations and their applications in day to day problems. In Class XI, we have studied linear inequalities and systems of linear inequalities in two variables and their solutions by graphical method. Many applications in mathematics involve systems of inequalities/equations. In this chapter, we shall apply the systems of linear inequalities/equations to solve some real life problems of the type as given below:

A furniture dealer deals in only two items–tables and chairs. He has Rs 50,000 to invest and has storage space of at most 60 pieces. A table costs Rs 2500 and a chair Rs 500. He estimates that from the sale of one table, he can make a profit of Rs 250 and that from the sale of one chair a profit of Rs 75. He wants to know how many tables and chairs he should buy from the available money so as to maximise his total profit, assuming that he can sell all the items which he buys.

Such type of problems which seek to maximise (or, minimise) profit (or, cost) form a general class of problems called optimisation problems. Thus, an optimisation problem may involve finding maximum profit, minimum cost, or minimum use of resources etc. A special but a very important class of optimisation problems is linear programming problem. The above stated optimisation problem is an example of linear programming problem.

Linear programming problems are of much interest because of their wide applicability in industry, commerce, management science etc. In this chapter, we shall study some linear programming problems and their solutions by graphical method only, though there are many other methods also to solve such problems.

### FAQs Related to NCERT Solutions for Class 12 Maths Chapter 12 PDF

**Q. Where can I get NCERT Solutions for Class 12 Maths PDF to download for all chapters?**A. Follow the link **NCERT Solutions for Class 12 Maths** to download for all chapters PDF on Embibe.

**Q. What are the exercises in NCERT Solutions for Class 12 Maths Chapter 12 PDF**?A. Here is the list of NCERT Solutions for Class 12 Maths Chapter 12 PDF

NCERT Solutions for Class 12 Maths Chapter 12 Exercise 12.1: Introduction

NCERT Solutions for Class 12 Maths Chapter 12 Exercise 12.2: Linear Programming Problem and its Mathematical Formulation

NCERT Solutions for Class 12 Maths Chapter 12 Exercise 12.3: Different Types of Linear Programming Problems

Miscellaneous

**Q. What is linear programming in Class 12?**

A. Linear programming is used for obtaining the best solution for a problem with given constraints. In linear programming, we formulate our real-life problem into a mathematical model. It involves an objective function, linear inequalities with subject to constraints.

**What are the major components of a linear program?**

A. The major components of linear program models have three major components: decision variables, objective function, and constraints

**Q. What are the characteristics of the linear programming problem?**

A. **Linearity** – The relationship between two or more variables in the function must be linear. It means that the degree of the variable is one.**Finiteness** – There should be finite and infinite input and output numbers

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