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?

(A) Maximum value of Z is at R(40, 0).

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

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

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

Answer 1

Correct option is (B) Maximum value of Z is at Q(30, 20)

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 so the maximum value of the objective function z = 180 is at Q(30, 20).