Question

The minimum value of z = 2x + 9y subject to constraints x + y ≥ 1, 2x + 3y ≤ 6, x ≥ 0, y ≥ 0 is ______.

Options

• 0

• 3

• 2

• 1

Answer 1

The minimum value of z = 2x + 9y subject to constraints x + y ≥ 1, 2x + 3y ≤ 6, x ≥ 0, y ≥ 0 is 2.

Explanation:

The feasible region lies non-origin side of line x + y = 1

and on origin side of line 2x + 3y = 6, in first quadrant.

The corner points of feasible region are

A (3, 0), B (0, 2), C (1, 0) and D (0, 1)

∴ At A (3, 0), z = 6

At B (0, 2), z = 18

At C (1, O),z=2

At D (0, 1), z = 9

 ∴  Minimum value of z is 2.