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Question

Minimise and Maximise of Z=5x+10y subject to x+2y120,x+y60,x2y0,x,y0

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Solution

The feasible region determined by the constraints, x+2y120, x+y60, x2y0,x0 and y0 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 pointZ=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)
1028553_422950_ans_d666ebb3523d4ef8ba657e039c6275e2.bmp

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