Demand for The Secret Loves of John O, a romance novel by Margó Dufón that flopped after two weeks on the market, is given by q = −2p2 + 7p + 8 (0 ≤ p ≤ 4.4) copies sold per week when the price is p dollars. Taking into account storage and shipping, it costs OHaganBooks.com C = 3q dollars to sell q copies of Margó Dufón's The Secret Loves of John O in a week. (a) Express the weekly profit P earned by OHaganBooks.com from the sale of The Secret Loves of John O as a function of unit price p. P(p) = (b) What price should the company charge to get the largest weekly profit? (Round your answer to the nearest cent.) $ What is the maximum possible weekly profit? (Round your answer to the nearest cent.) $ (c) Compare your answer in part (b) with the price the company should charge to obtain the largest revenue, $2.81. Explain any difference. At the price the company should charge to obtain the highest revenue, the cost per book is ---Select--- decreasing with the increasing price increasing with increasing price neither increasing nor decreasing, while the revenue is ---Select--- decreasing with increasing price increasing with increasing price neither increasing nor decreasing. Thus the profit is ---Select--- decreasing with increasing price increasing with increasing price neither increasing nor decreasing, suggesting that the maximum profit will occur at ---Select--- a lower price this price a higher price. This is ---Select--- inconsistent consistent with what we found in (b).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Demand for The Secret Loves of John O, a romance novel by Margó Dufón that flopped after two weeks on the market, is given by

q = −2p² + 7p + 8 (0 ≤ p ≤ 4.4)

copies sold per week when the price is p dollars.

Taking into account storage and shipping, it costs OHaganBooks.com

C = 3q

dollars to sell q copies of Margó Dufón's The Secret Loves of John O in a week.

(a)

Express the weekly profit P earned by OHaganBooks.com from the sale of The Secret Loves of John O as a function of unit price p.

P(p) =

(b)

What price should the company charge to get the largest weekly profit? (Round your answer to the nearest cent.)

What is the maximum possible weekly profit? (Round your answer to the nearest cent.)

(c)

Compare your answer in part (b) with the price the company should charge to obtain the largest revenue, $2.81. Explain any difference.

At the price the company should charge to obtain the highest revenue, the cost per book is ---Select--- decreasing with the increasing price increasing with increasing price neither increasing nor decreasing, while the revenue is ---Select--- decreasing with increasing price increasing with increasing price neither increasing nor decreasing. Thus the profit is ---Select--- decreasing with increasing price increasing with increasing price neither increasing nor decreasing, suggesting that the maximum profit will occur at ---Select--- a lower price this price a higher price. This is ---Select--- inconsistent consistent with what we found in (b).

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