Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C (x) equals0.2xsquaredminus0.4xplus6.636 , where C (x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?

100 bicycles

Step-by-step explanation:

If C (x) = 0.2x²-0.4x+6.636

The general form of a quadratic expression is given as: ax²+bx+c

Therefore from C (x),

a=0.2, b=-0.4, c=6.636.

C (x) is a parabola with its "a" coefficient 0.2 being positive so the curve opens upward indicating that the vertex is a minimum.

We simply need to find the vertex of:

C (x) = 0.2x²-0.4x+6.636

This occurs when:

x = - b / (2a)

x = - (-0.4) / (2*0.2)

x = (0.4) / (0.4)

x = 1

Since x=1 at the vertex, the company should build 100 bicycles to minimize the average cost per bicycle.