Question 598646: Aki's bicycle design has determined that when x hundred bicycles are built, the average cost of bicycles is given by C(x)=0.2x^2-1.8x+8.815, where C(x) is in hundreds of dollars. How Many bicycles should the shop build to minimize the average cost per bicycle?
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Aki's bicycle design has determined that when x hundred bicycles are built, the average cost of bicycles is given by C(x)=0.2x^2-1.8x+8.815, where C(x) is in hundreds of dollars. How Many bicycles should the shop build to minimize the average cost per bicycle?
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Looking at:
C(x)=0.2x^2-1.8x+8.815
We know the minimum is at the vertex because the equation is a quadratic (2nd degree) thus in a form of a parabola that opens upwards (since the coefficient associated with the x^2 term is positive).
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The x value of the vertex is at:
x = -b/(2a)
x = -(-1.8)/(2(0.2))
x = 1.8/0.4
x = 4.5
answer:
cost is minimized when you build 450 (4.5*100)bicycles
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