Question 1057794: Please I am in need of the following word problem really appreciate your help
A shoe company produces basketball and aerobics shoes. Each shoe is partially assembled by machine and then finished by hand. An aerobic shoe takes 0.25 hours to produce by machine and 0.1 hours to produce by hand. A basketball shoe takes 0.15 hours to assemble by machine and 0.2 hours to assemble by hand. Each day, the company can afford up to 900 machine hours and up to 500 hours to be complete by hand. If the company makes $10 from each aerobic and $15 from each basketball shoe, how many of each should be produced to maximize profits?
I am having difficulty creating the table or chart and then graphing it
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A shoe company produces basketball and aerobics shoes. Each shoe is partially assembled by machine and then finished by hand. An aerobic shoe takes 0.25 hours to produce by machine and 0.1 hours to produce by hand. A basketball shoe takes 0.15 hours to assemble by machine and 0.2 hours to assemble by hand. Each day, the company can afford up to 900 machine hours and up to 500 hours to be complete by hand. If the company makes $10 from each aerobic and $15 from each basketball shoe, how many of each should be produced to maximize profits?
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Profit Eq:: P = 10a + 15b dollars
Machine time Eq:: 0.25a + 0.15b <= 900 machine hrs
Hand time Eq::::: 0.10a + 0.20b <= 500 hand hrs
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Modify the equations:
a <= (-0.15/0.25)b + 900/0.25
a <= (-0.20/0.10)b + 500/0.10
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a <= -0.6b + 3600
a <= -2b + 5000
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Find the intersection::
-0.6b + 3600 = -2b + 5000
1.4b = 1400
b = 1000
Find "a":
a = -2b+5000 = 3000
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Vertices to check in the Profit Equation::
(0,3600) ; (1000,3000), (2500,0)
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P = 10a + 15b
(0,3600)::: P = 15*3600 = 54000
(1000,3000):: P = 10*1000 + 15*3000 = 55000
(2500,0) ::: P = 10*2500 = 25000
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The winner:: a = 1000 ; b = 3000
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Cheers,
Stan H.
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