Question

If 4x + 5y ≤ 20, x + y ≥ 3, x ≥ 0, y ≥ 0, maximum 2x + 3y is ______.

Options

• 12

• 5

• 0

• 20

Answer 1

If 4x + 5y ≤ 20, x + y ≥ 3, x ≥ 0, y ≥ 0, maximum 2x + 3y is 12.

Explanation:

The feasible region lies on origin side of 4x + 5y = 20, non-origin side of x + y = 3 and in first quadrant.

∴ The corner points of feasible region are A(5, 0), B(O, 4), C(3, 0) and D(O, 3)

∴ Maximum 2x + 3y is at B(0, 4)

∴ Maximum 2x + 3y = 2(0) + 4(3) = 12