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4. A company is launching a new line of electronic gadgets. The number of units sold, n, is a function of the price per unit, p, given by n(p) = 50 - 20p. The cost c to produce n units is given by c(n) = 200 + 5n, and the revenue r from selling n units is given by r(n) = 500n - - 10n². a. Express the cost function c in terms of the price p. b. Express the revenue function r in terms of the price p. c. Find the profit function π in terms of the price p, where profit is defined as revenue minus cost. d. Determine the price p that maximizes the profit.

4. A company is launching a new line of electronic gadgets. The number of units sold, n, is a function of the price per unit, p, given by n(p) = 50 - 20p. The cost c to produce n units is given by c(n) = 200 + 5n, and the revenue r from selling n units is given by r(n) = 500n - - 10n². a. Express the cost function c in terms of the price p. b. Express the revenue function r in terms of the price p. c. Find the profit function π in terms of the price p, where profit is defined as revenue minus cost. d. Determine the price p that maximizes the profit.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 43E
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4. A company is launching a new line of electronic gadgets. The number of units sold, n, is a function of the price per unit, p, given by n(p) = 50 - 20p. The cost c to produce n units is given by c(n) = 200 + 5n, and the revenue r from selling n units is given by r(n) = 500n - - 10n². a. Express the cost function c in terms of the price p. b. Express the revenue function r in terms of the price p. c. Find the profit function π in terms of the price p, where profit is defined as revenue minus cost. d. Determine the price p that maximizes the profit.
Transcribed Image Text:4. A company is launching a new line of electronic gadgets. The number of units sold, n, is a function of the price per unit, p, given by n(p) = 50 - 20p. The cost c to produce n units is given by c(n) = 200 + 5n, and the revenue r from selling n units is given by r(n) = 500n - - 10n². a. Express the cost function c in terms of the price p. b. Express the revenue function r in terms of the price p. c. Find the profit function π in terms of the price p, where profit is defined as revenue minus cost. d. Determine the price p that maximizes the profit.
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