Question 142102
acme cycle shop stocks two models of bicycles.
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one model costs the shop $100, and the other model costs $200
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the profit on the $100 model $50. the profit on the $200 model is $75.
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a) if the number of $100 bikes is x, and the number of $200 bikes is y, write an inequaltiy that states that the display space has room for no more than 20 bikes.
x + y <= 20
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b)write an inequality that states that the store cannot pay more than $3200 for their stocks of bikes.
100x + 200y <= 3200
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c)write inequalities that state that the store cannot sell negative nubers of bikes. 
x >= 0 ; y >= 0
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d)if the profit of the $100 bikes is $50, and the profit on the $200 model is $75, write the profit function P(x,y) 
P(x,y) = 50x + 75y
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e) graph the comstraints 
y <= 20-x
y <= 16-(1/2)x
{{{graph(400,300,-10,45,-10,45,16-(1/2)x,20-x)}}}
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f) how many of each should the shop order to make the maximun profit?
Find the coordinates of the vertices of the area inclosed in the 1st quadrant:
(0,0), (0,16),(8,12), (20,0)
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Substitute each of these x/y pairs into the profit equation to see 
which pair gives the maximum profit:P(x,y) = 50x + 75y
(0,0) doesn't
(0,16) gives 75*16 = 1200
(8,12) gives 50*8+12*75 = 1300
(20,0) gives 50*20 = 1000 
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So 8 of the 100 dollar and 12 of the 200 dollar gives the maximum profit.
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Cheers,
Stan H.