The total cost (m hundreds of dollars) to produce x units of a product is C(x) = 4x − 92x + 1C(x) = 4x − 92x + 1

a)

The average cost at 15 units is the total cost at 15 units divided by 15.

C(15)=4∗15−92∗15+1=1.645Avg=1.645/15=0.120C(15)=4∗15−92∗15+1=1.645Avg=1.645/15=0.120

b)

The average cost for x units is just the cost function divided by x. This is the average cost function.

Avg=( 4x − 92x + 1)/xAvg=4x−92x2+xAvg=( 4x − 92x + 1)/xAvg=4x−92x2+x

c)

The marginal average cost function will be the derivative of the average cost function.

Avg=4x−92x2+xUsing theuvrule of differentiation:MAC=Avg′=(4x−9)∗(4x+1)−{(2x2+x)∗4}(2x2+x)2=16x2+4x−36x−9−8x2−4x(2x2+x)2=8x2−36x−9(2x2+x)2