Compute the marginal cost at q 30 how does this relate to

Question

Question: Involve the average cost of manufacturing a quantity q of a good, which is defined to be

a(q) = C(q)/q

The average cost per item to produce q items is given by

a(q) = 0.01q² - 0.6q + 13, for q > 0

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

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

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

(d) Compute the marginal cost at q = 30. How does this relate to your answer to part (c)? Explain this relationship both analytically and in words.