The average cost per item to produce q items is given by: a(q) = .01q 2 - 0.6q +

Question

The average cost per item to produce q items is given by: a(q) = .01q2 - 0.6q + 24, for q > 0.

a) What is the total cost, C(q), of producing q goods?

C(q) =

b) What is the minimum marginal cost? What is the practival interpretation of this result?

The mimimum marginal cost is $ ___________________.

This means that the marginal cost is at a ____________ when the additional cost per item is $ _______________

c) At what production level is the average cost a minimum? What is the lowest average cost?

The production level at which the average cost is a minimum is _________________

The lowest average cost is $_______________ per item.

d) Compute the marginal cost at q= 30. How does this relate to your answer to part c.

The marginal cost at q=30 is $ _______________________

Explanation / Answer

a) total cost = average cost per item * number of items --> c(q) = a(q) * q -->

c(q) = .01q^3 - .6q^2 + 13q

b) marginal cost = c'(q)
c'(q) = .03q^2 - 1.2q + 13
The marginal cost and the average cost will equal when either q = 0 or q = 30. If production is between these points, marginal cost < average cost.

c) average cost is minimized when a'(q) = 0.
a'(q) = .02q - .6 = 0 --> q = 30. At this level, average cost = 4

d) marginal cost at q = 30 --> c'(30) = 4, which matches the result we already found.

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