Question

The maximum of z = 5x + 2y, subject to the constraints x + y ≤ 7, x + 2y ≤ 10, x, y ≥ 0 is ______.

Options

• 10

• 26

• 35

• 70

Answer 1

The maximum of z = 5x + 2y, subject to the constraints x + y ≤ 7, x + 2y ≤ 10, x, y ≥ 0 is 35.

Explanation:

Feasible region lies on origin side of x + y = 7 and x + 2y = 10, and in first quadrant.

The corner points of feasible region are 0(0, 0), A(7, 0), E(4, 3) and D(O, 5)

∴ Maximum z = 5x + 2y is at A(7, 0)

∴ Maximum, z = 5(7) + 2(0) = 35