Suppose that when the price of a certain commodity is p dollars per unit, then x hundred units is C(x) = 0.02x^2 +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