Question 140853
A clothing manufacturer has 100 m of silk and 180 m of wool. 
To make a suit it requires 2m of silk and 3m of wool, 
to make a dress 1m of silk and 2m of wool. 
If the profit on the suit is $108 and the profit on the dress is $60, 
how many suits and dresses should be made to maximize the profit? 
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Let # of suits be "s"; Let # of dresses be "d":
Profit = 108s + 60d
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Silk: 2s + d <= 100
Wool: 3s +2d <= 180
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Solve both for d and graph them:
d <= -2s + 100
d <= (-3/2)s + 90
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{{{graph(400,300,-10,100,-10,200,-2x+100,(-3/2)x + 90)}}}
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Find the coordinates of the enclosed polygon and test the
coordinates in the Profit equation to determine the maximum.
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Coordinates: (20,60), (0,0) , (0,90), (50,0)
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Determining maximum Profit:
Profit = 108s + 60d 
(20,60): P = 108*20 + 60*60 = 5760
(0,90): P = 90*60 = 5400
(50,0): p = 50*108 = 5400
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Maximum profit comes when 20 dresses and 60 suits are produced
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Cheers,
Stan H.