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Aki’s bicycle designs has determined that when x hundred bicycles are built, the average cost per...

Aki’s bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.2x^2-0.1x+5.857, where C(x) is in hundreds of dollars.

How many bicycles should the shop build to minimize the average cost per bicycle?

Expert Solution

Average cost per hundred bicycle is given by

, where C(x) is the average cost in hundreds of dollars and x is the number of bicycles in hundreds

We need to minimize this function

We know a maxima or minima occurs when the slope changes, and we know that the slope changes when the derivative is zero.
That is

Will be zero

That is

We have to then take to double derivative to check whether it is a maxima or a minima at that value of x,it will be a maxima when the double derivative is negative and it will be a minima when the double negative is positive. That is

Hence, it will be a minima at

Hence, 0.25 hundred bicycles, or bicycles should be built to minimize costs.

milcah answered 2 years ago

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