9. (15 pts) See textbook page 82 for a summary of the economic functions (price-demand p, revenue R, cost C, average cost , and profit P ) used in this problem. The cost, in dollars, for a company to produce x widgets is given by C(x) = 5000 + 3.00x for x 0, and the price-demand function, in dollars per widget, is p(x) = 28 - 0.02x for 0 x 1400.

(a) Find and interpret C(800).

(b) Find and interpret (800). (Note that (x) is the average cost function.)

(c) Find and simplify the expression for the revenue function R(x). (work optional)

(d) Find and simplify the expression for the profit function P(x). (work optional) Note that p(x) and P(x) are different functions.

(e) Find and interpret P(800), where P(x) is the profit function in part (d).