Question

The maximum value of P = 7x + 6y subject to constraints x + 2y ≤ 24, 2x + y ≤ 30 and x ≥ 0, y ≥ 0 is ______.

Options

• 90

• 120

• 96

• 240

Answer 1

The maximum value of P = 7x + 6y subject to constraints x + 2y ≤ 24, 2x + y ≤ 30 and x ≥ 0, y ≥ 0 is 120.

Explanation:

The feasible region lies on the origin side of
x +2y = 24 and
2x + y = 30, in the first quadrant.

The corner points of the feasible region are O

(0, 0), A (15, 0),

B (0, 12) and C (12, 6)

At A(15 , 0), z = 105

At B(0, 12), z = 72

At C(12, 6),

z = 120

∴ Maximum value of z is 120.