Your college newspaper, The Collegiate Investigator, sells for 900 per copy. The

Question

Your college newspaper, The Collegiate Investigator, sells for 900 per copy. The cost of producing x copies of an edition is given by C(x) = 70 + 0.10x + 0.001x^2 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. The approximate 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.

Explanation / Answer

(a) Price p(x)=0.9x

C(x)= 70+0.1x+0.001x^2

R(x)=p(x)-C(x)

R(x) = 0.8x-70-0.001x^2

R'(x)=0.8-0.002x

P'(x)=0.9

R(500)=80

P(500)=450

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