Question

Minimise and Maximise Z = 5x + 10y

subject to  x+2y≤ 120,x+y≥60,x-2y≥0,x,y≥0 

Answer 1

The feasible region determined by the constraints, x+ 2y ≤ 120, x + y ≥   60, x − 2y≥  0,   x ≥ 0, and y ≥ 0, is as follows. 

The corner points of the feasible region are A (60, 0), B (120, 0), C (60, 30), and D (40, 20).
The values of Z at these corner points are as follows.

The minimum value of Z is 300 at (60, 0) and the maximum value of Z is 600 at all the points on the line segment joining (120, 0) and (60, 30).