Question

For the linear programming problem (LPP), the objective function is Z = 4x + 3y and the feasible region determined by a set of constraints is shown in the graph:

Which of the following statements is true?

पर्याय

• Maximum value of Z is at R(40, 0).

• Maximum value of Z is at Q(30, 20).

• Value of Z is at R(40, 0) is less than the value at P(0, 40).

• Value of Z is at Q(30, 20) is less than the value at R(40, 0).

Answer 1

Maximum value of Z is at Q(30, 20).

Explanation:

	Corner point	Value of the objective function Z = 4x + 3y
1.	O(0, 0)	Z = 0
2.	R(40, 0)	Z = 160
3.	Q(30, 20)	Z = 120 + 60 = 180
4.	P(0, 40)	Z = 120

Since the feasible region is bounded, the maximum value of the objective function Z = 180 is at Q(30, 20).