In Exercises 17 through 22, you are given the price p(q) at which q units of a particular commodity can be sold and the total cost C(q) of producing the q units. In each case:

(a) Find the revenue function R(q), the profit function P(q), the marginal revenue R'(q), and marginal cost C'(q). Sketch the graphs of P(q), R'(q), and C'(q) on the same coordinate axes and determine the level of production q where P(q) is maximized.

(b) Find the average cost A(q) = C(q)/q , and sketch the graphs of A(q), and the marginal cost C'(q) on the same axes. Determine the level of production q at which A(q) is minimized.

p(q) = 49 − q; C(q) = 1/8q² + 4q + 200