In class 11th we already study linear inequalities and their solutions by the graphical method and also learnt systems of linear equations and their applications in daily life problems. In maths chapter 12 Linear programming we are going to deal with problems on linear programming like maximization and minimization of equations. In this chapter, there are 2 exercises with 21 questions. The NCERT Solutions for Class 12 Maths Chapter12 Linear Programming are prepared and solved by subject experts for the students to score well with good marks in the board exam as well as in the competitive exams.
In NCERT Class 12 Maths Chapter12 Linear Programming, we will apply the systems of linear equations/inequalities to solve some reallife problems. Let's take an NCERT problem  A furniture dealer deals in only two items–chairs and tables. Has storage space of at most 60 pieces and He has Rs 50,000 to invest. A chair costs Rs 500 and A table costs Rs 2500. He estimates that from the sale of one chair, he can make a profit of Rs 75 and that from the sale of one table a profit of Rs 250. He wants to know how many chairs and tables 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.
That type of problems which involve minimize profit or maximize cost is called optimisation problems. Linear programming problems are a very important class of optimisation problems. The abovestated problem is an example of linear programming. Class 12 NCERT Maths Chapter12 Linear Programming is an important chapter because of their wide applicability in industry, management science, commerce, etc. In this chapter, we will learn mathematical and graphical methods to solve problems of linear programming.
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
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming Exercise Questions
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming Exercise 12.1
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming Exercise 12.2
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming Miscellaneous
Chapter 1 

Chapter 2 

Chapter 3 

Chapter 4 

Chapter 5 

Chapter 6 

Chapter 7 

Chapter 8 

Chapter 9 

Chapter 10 

Chapter 11 

Chapter 13 
11. The corner points of the feasible region determined by the following system of linear inequalities:
are and . Let where Condition on p and q so that the maximum of Z occurs at both and is
10.A toy company manufactures two types of dolls, A and B. Market research and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on dolls A and B, how many of each should be produced weekly in order to maximise the profit?
6. Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively. They supply to 3 ration shops, D, E and F whose requirements are 60, 50 and 40 quintals respectively. The cost of transportation per quintal from the godowns to the shops are given in the following table:
Transportation cost per quintal (in Rs)  
From/To  A  B 
D  6  4 
E  3  2 
F  2.50  3 
How should the supplies be transported in order that the transportation cost is minimum? What is the minimum cost?