Answer to Question #274849 in Calculus for sumu

Question

Your firm has recently started to give economic advice to your clients. Acting as a consultant you have estimated the demand curve of a client’s firm to be

AR = 200 - 8x where AR is average revenue ($) and x is output.

Investigation of the client firm’s cost profile shows that the marginal cost is given by: MC = x2 - 28x + 211 where MC is marginal cost ($). Further investigation has shown that the firm’s cost when no production are $10.

(a) Find equation of total cost.

(b) If total revenue is average revenue multiplied by output, find the equation of total revenue.

(c) Use the methods of differentiation, find the turning point(s) of the firm’s profit curve and say whether these point(s) are maxima or minima.

(d) Determine the level of production to give maximum or minimum profit. Find the profit.

(e) Find the equation of marginal revenue and determine the marginal revenue at output level of 20 units.

5. Suppose you plan to set up a firm to retail a certain product A. From