NCERT Book Class 12 Maths Chapter 12 Linear Programming

394 MATHEMATICS

Chapter 12
LINEAR PROGRAMMING

v The mathematical experience of the student is incomplete if he never had
the opportunity to solve a problem invented by himself. – G. POLYA v

12.1 Introduction
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 L. Kantorovich
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.