Question

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

Explanation:

Change the inequalities into equations and draw the graph of lines, thus we get the required feasible region as shown below.

The region bounded by the vertices A(0, 5), B(4, 3), C(7, 0).

The objective function is maximum at C(7, 0) and Max z = 5 × 7 + 2 × 0 = 35.