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, y≥0, is as follows.

The corner point 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).