Question 142102: IS THERE ANYONE WHO CAN HELP ME WITH THIS????
acme cycle shop stocks two models of bicycles.one model costs the shop $100, and the other model costs $200. the profit on the $100 model $50. the profit on the $200 model is $75.
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.
b)write an inequality that states that the store cannot pay more than $3200 for their stocks of bikes.
c)write inequalities that state that the store cannot sell negative nubers of bikes.
d)if the profit of the $100 bikes is $50, and the profit on the $200 model is $75, write th eprofit function P(x,y)
e) graph the comstraints
f) how many of each should the shop order to make the maximun profit?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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
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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.
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