Suppose that when the price of a certain commodity is p dollars per unit, then x hundred units will be purchased by consumers, where p = −0.05x + 38. The cost of producing x hundred units is C(x) = 0.02x² + 3x + 574.77 hundred dollars.

a. Express the profit P obtained from the sale of x hundred units as a function of x. Sketch the graph of the profit function.

b. Find the average profit AP when the price is $37 per unit.

c. Use the profit curve found in part (a) to determine the level of production x that results in maximum profit. What unit price p corresponds to maximum profit?