Question

Maximise Z = -x + 2y, subject to the constraints: x ≥ 3, x + y ≥ 5 , x + 2y ≥ 6, y ≥ 0

Answer 1

x + y = 5

x	1	3	2
y	4	2	3

0 + 0 5 

False 

0  3 False

x + 2y = 6

x	0	4	2
y	3	1	2

0 + 0  False 

ABC is the solution region 

At A (3,2) Z =-3+2 x 2=1 

At B (4,1) Z = -4 + 2 x 1 = -2 

At C (6, 0) Z = -6 = -6 

Z is maximised at A (3, 2) = 1 and 

minimised at C (6, 0) = -6