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# Chapter 12 Linear Programming

Linear programming is a method in which we represent problems with the help of graphs. It will enhance our practical understanding toward problems. This chapter consists of definitions of related terminology such as constraints, objective function, optimization, different types of linear programming problems, mathematical formulation graphical methods, feasible and infeasible regions and solutions, optimal feasible solutions.

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### Exercise 1

• Q1 Maximise Z = 3x + 4y Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
Ans:

The feasible region determined by the constraints, x + y ≤ 4, x ≥ 0, y ≥ 0, is as follows.

The corner points of the feasible region are O (0, 0), A (4, 0), and B (0, 4). The values of Z at these points are as follows.

 Corner point Z = 3x + 4y O(0, 0) 0 A(4, 0) 12 B(0, 4) 16 → Maximum

Therefore, the maximum value of Z is 16 at the point B (0, 4).

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