MAXIMUM PROFIT AND MINIMUM AVERAGE COSTIn Exercises22, you are given the price p(q) at whi...

MAXIMUM PROFIT AND MINIMUM AVERAGE COSTIn Exercises22, 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.