Question

Minimise and Maximise Z=x+2y
Subject to x+2y≥100,2x-y≤0,2x+y≤200;x,y≥0.

Answer 1

The feasible region determined by the constraints,x+2y≥100,2x-y≤0,2x+y≤200,x≥0,and y≥0,is as follows.

The corner points of the feasible region are A(0,50),B(20,40),C(50,100),and D(0,200)

The value of Z at these corner points is as follows.

The maximum value of Z is 400 at (0,200) and the Minimum value of Z is 100 at all the points on the line segment joining the points (0,50)and(20,40).