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Question 136907: Aki's Bicycle Design has determined that when x hundred bicyles are built, the average cost per bicycle is given by C(x)=0.4x^2-0.9x+2.573, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?
I understand that I need to re-write into y=a(x-b)^2+K where x=h.
I start out with c(x)=0.4x^2...(am I supposed to round 0.9 up to 3 decimal places..?) +2.573. The rounding part is completely throwing me off.
Please help me understand this problem. Thank you.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Aki's Bicycle Design has determined that when x hundred bicyles are built, the average cost per bicycle is given by C(x)=0.4x^2-0.9x+2.573, where C(x) is in hundreds of dollars.
How many bicycles should the shop build to minimize the average cost per bicycle?
The equation is a quadratic with a=0.4 and b=-0.9
The minimum value occurs when x = -b/2a = 0.9/(0.8) = (9/8)
(9/8)*100 = 112.5 (# of bikes they should make to minimize cost)
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I understand that I need to re-write into y=a(x-b)^2+K where x=h.
Completing the square on 0.4x^2-0.9x+2.573 = y
0.4(x^2-(0.9/0.4)x = y-2.573
0.4(x^2-(9/4)x+(9/8)^2) = y-2.573+0.4*(9/8)^2
0.4(x-(9/8))^2 = y - 2.06675
So h=(9/8) and (9/8)*100 = 112.5 bikes to minimize cost
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Cheers,
Stan H.
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