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.