Chapter 4.5, Problem 26E

Problems 25–26 involve the average cost of manufacturing a quantity q of a good, which is defined to be

$a(q)=\frac{C(q)}{q}.$

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

$a(q)=0.01q^2-0.6q+13,\mathrm{for}q>0.$

1. (a) What is the total cost, C(q), of producing q goods?
2. (b) What is the minimum marginal cost? What is the practical interpretation of this result?
3. (c) At what production level is the average cost a minimum? What is the lowest average cost?
4. (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.