x + 2y = 120
0 + 0 < 120 True x + y = 60
0 + 0 0 false
x – 2y =0
40 – 20 > 0
ABCD is the solution region
At A (60, 30) Z = 5 x 60 + 10 x 30 = 600
At B (40, 20) Z = 5 x 40+10 x 20 = 400
At C (60,0) Z = 5 x 60 = 300
At D (120,0) Z = 5 x 120 = 600
Z is minimized at C (60,0) = 300
Z is maximized at 2 points A (60,30), D (120,0)
∴ maximum value is 600 at all
points on the line joining A (60,30) and D (120,0)