Minimize and Maximize Z = 5x + 10 y subject to x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x, y ≥ 0.

It is given in the question that,

Minimize and Maximize, Z = 5x + 10y

We have to subject on the following equation:

(x, y) = (0, 60), (120, 0)

(x, y) = (0, 0), (20, 10)

(x, y) = (60, 0), (0, 60)

∴ It is clear that at (60, 0) Z has its minimum value i.e. 300

Also, Z is minimum at two pints (60, 30) and (120, 0)

Hence, the value of Z will be maximum at all points joining (60, 30) and (120, 0)