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Question

Maximize Z=12x+24y subject to the constraints x+y5,5x+7y35,xy0,x,y0 graphically.

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Solution

Z=12x+24y(Given)
Subject to the constraints:
x+y5
5x+7y35
xy0
x,y0
Case I:- x+y5
x0 5
y50
Case II:- 5x+7y35
x0 7
y5 0
Case II:- xy0
x0 1
y0 1
MaxZ=12x+24y
Corner points Value of Z
(52,52)90
(2.9,2.9) 104.4
(5,0)
60
(7,0)
84
MaxZ=104.4 when x=y=2.9.
Hence the maximum value of Z is 104.4.

1211698_1512665_ans_36afff103a1e4419b38651a4232033d6.jpeg

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