Question

Minimise and Maximise Z = x + 2y 

subject to x + 2y ≥ 100, 2x – y ≤ 0, 2x + y ≤ 200; x, y ≥ 0.

Answer 1

x + 2y = 100

x	100	50	20
y	0	20	40

0 + 0  100 

0 – 0 < 0 

False 2x – y = 0

x	100	20	10
y	200	40	20

0 – 0 < 0 

False 

2x +y = 200

x	100	50	60
y	0	100	80

0 + 0 <200 True

ABCD is the solution . 

At A (0,200), Z = 2 x 200 = 400 

At B (50,100), Z = 50 + 2 x 100 = 250 

At C (20,40), Z = 20 + 2x 40= 100 

At D (0,50), Z = 2 x 50 =100 

Z is maximised at A (0,200) = 400 

Z is minimised at 2 points C (20,40) & D (0, 50) = 100