Your college newspaper, The Collegiate Investigator, sells for 90 per copy. The cost of producing x copies of an edition is given by C(x) = 30 + 0.10x + 0.001x2 dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.] R'(x) = P'(x) = (b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 500 copies of the latest edition.

revenue_______ $

profit ________ $

marginal revenue ______ $ per additional copy

marginal profit ________ $ per additional copy

Interpret the results. The approximate ---Select---(profit, loss) from the sale of the 501st copy is $_____ .

(c) For which value of x is the marginal profit zero? x = _____ copies

Interpret your answer. The graph of the profit function is a parabola with a vertex at x = ________ , so the profit is at a maximum when you produce and sell ________copies.