A certain product is available in two versions: an ordinary one and a luxury version. Market research shows that a total of 20 000 people will buy the product, and that their decision about the version is determined by the prices. The relation between the amounts sold of the two versions (91 and 92, respectively) and the unit prices (p₁ and p2) is given by 91 = 40 000-2p₁ and 92 = 20 000+P₁-P2- a. Translate the information that a total of 20 000 people will buy the product into an equation relating the unit prices p₁ and p2. b. Set up an equation for the total revenue r in terms of p₁. c. Use the first and second derivative to determine p₁ such that the revenue is maximal. d. Check your result by making the graph of the function r(p₁).

A certain product is available in two versions: an ordinary one and a luxury version. Market research shows that a total of 20 000 people will buy the product, and that their decision about the version is determined by the prices. The relation between the amounts sold of the two versions (91 and 92, respectively) and the unit prices (p₁ and p2) is given by 91 = 40 000-2p₁ and 92 = 20 000+P₁-P2- a. Translate the information that a total of 20 000 people will buy the product into an equation relating the unit prices p₁ and p2. b. Set up an equation for the total revenue r in terms of p₁. c. Use the first and second derivative to determine p₁ such that the revenue is maximal. d. Check your result by making the graph of the function r(p₁).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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