Question

Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.5x^2 -1.3x+9.972, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle? ...?

Answer 1

The minimum of the cost can be found by differentiating the cost equation with respect to the number of bicycles and then equating the differential to 0.
0 = x -1.3
x= = 1.3
0.3 cycles cannot be built, so the company should make 1 bicycle to minimize cost.