The long-run total cost function for a firm producing skateboards is

TC = q3 – 40q2 + 430q

Where q is the number of skateboards per week.

a. What is the general shape of this total cost function?

b. Calculate the average cost function for skateboards. What shape does the graph of this function have? At what level of skateboard output does average cost reach a minimum? What is the average cost at this level of output?

c. The marginal cost function for skateboards is given by

MC = 3q2 – 80q + 430

Show that this marginal cost curve intersects average cost at its minimum value.

d. Graph the average and marginal cost curves for skateboard production.