Question

The maximum value of P = 3x + 4y subject to the constraints x + y ≤ 40, x + 2y ≤ 60, x ≥ 0 and y ≥ 0 is ______ 

Options

• 120

• 140

• 100

• 160

Answer 1

The maximum value of P = 3x + 4y subject to the constraints x + y ≤ 40, x + 2y ≤ 60, x ≥ 0 and y ≥ 0 is 140.

Explanation:

The feasible region lies on the origin side of x + y = 40 and x + 2y = 60, in first quadrant.

The comer points of the feasible region are

O(0, 0), A(0, 30), B(20, 20) and C(40, 0)

∴ At A(0, 30), P = 0 + 4 (30) = 120

At B(20, 20), P = 3(20) + 4(20) = 140

At C(40, 0), P = 3(40) + 0 = 120

∴ Maximum value of P is 140.