Question 1129704: suppose a shoe factory produces both low grade and high grade shoes. the factory produces at least twice as many low grade as high grade shoes. the maximum possible production is 500 Pairs of shoes. a dealer calls for delivery of at least 100 high grade pairs of shoes per day. suppose the operation makes a profit of birr 2.00 per a pair of shoes on high grade shoes and birr 1.00 per pairs of shoes on low grade shoes. how many pairs of shoes of each type should be produced for maximum profit?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! suppose a shoe factory produces both low grade and high grade shoes. the factory produces at least twice as many low grade as high grade shoes. the maximum possible production is 500 Pairs of shoes. a dealer calls for delivery of at least 100 high grade pairs of shoes per day. suppose the operation makes a profit of birr 2.00 per a pair of shoes on high grade shoes and birr 1.00 per pairs of shoes on low grade shoes. how many pairs of shoes of each type should be produced for maximum profit?
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Equations::
L = 2H
L + H <= 500
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H >= 100
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Profit:: P = 2H + L
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On a L/H coordinate system graph the following
H is the vertical axis; L is the horizontal axis.
L + H <=500
H >= 100
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Find the vertices of the resulting enclosed area.
Vertices are (0,500) ; (200,0) ; (0,0)
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Check the profit at each vertex::
(0,500) yields P = 2H+L = 2*500 + 0 = $1000
(200,100) yields P = 2H+L =2*100 + 200 = $400
(0,0) yields P = 2H+L = 0
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Conclusion: He should produce 500 high grade shoes and 0 low grade shoes
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Cheers,
Stan H.
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