Minimise and Maximise of Z=5x+10y subject to x+2y≤120,x+y≥60,x−2y≥0,x,y≥0
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Solution
The feasible region determined by the constraints, x+2y≤120, x+y≥60, x−2y≥0,x≥0 and y≥0 is as given. The corner points 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:
Corner point
Z=5x+10y
A(60,0)
300
→ Minimum
B(120,0)
600
→ Minimum
C(60,30)
600
→ Minimum
D(40,20)
00
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)