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^2-1.1x+10.592, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?

We will solve this by finding the derivative of the C(x) function which will give us the instantaneous slope. Thereafter, we will find the extremas which will occur when the instantaneous slope is equal to 0.

Thus, derivative of C(x) is;

C'(x) = 0.4x - 1.1

Equating to zero, we can find the extremas.

Thus;

0.4x - 1.1 = 0

x = 1.1/0.4

x = 2.75

To check if this is minimum of maximum, we will find the second derivative of C(x)

Thus;

C''(x) = 0.4

Thus is a positive value, and so it means the critical point is a minimum.

Thus, X = 2.75

We were told x is in hundreds of bicycles. Thus, X = 2.75 × 100 = 275 bikes

​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^2-1.1x+10.592​, 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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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^2-1.1x+10.592, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?