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The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, produced by Phonola Media, is related to the price per compact disc. The equation p = 0.00038x + 7 (0 ≤ x ≤ 12,000) where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by C(x) = 600 + 2x - 0.00001x² (0 ≤ x ≤ 20,000). Hint: The revenue is R(x) = px, and the profit is P(x) = R(x) - C(x). Find the revenue function, R(x) = px. R(x) = Find the profit function, P(x) = R(x) - C(x). P(x) = Find the derivative of the profit function, P(x). P'(x) = Find the critical number of the function P(x). (Round your answer to the nearest whole number.) X = To maximize its profits, how many copies should Phonola produce each month? (Round your answer to the nearest whole number.) discs/month

The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, produced by Phonola Media, is related to the price per compact disc. The equation p = 0.00038x + 7 (0 ≤ x ≤ 12,000) where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by C(x) = 600 + 2x - 0.00001x² (0 ≤ x ≤ 20,000). Hint: The revenue is R(x) = px, and the profit is P(x) = R(x) - C(x). Find the revenue function, R(x) = px. R(x) = Find the profit function, P(x) = R(x) - C(x). P(x) = Find the derivative of the profit function, P(x). P'(x) = Find the critical number of the function P(x). (Round your answer to the nearest whole number.) X = To maximize its profits, how many copies should Phonola produce each month? (Round your answer to the nearest whole number.) discs/month

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.8: Joint And Combined Variation
Problem 5P
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The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, produced by Phonola Media, is related to the price per compact disc. The equation p = 0.00038x + 7 (0 ≤ x ≤ 12,000) where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by C(x) = 600 + 2x 0.00001x² (0 ≤ x ≤ 20,000). Hint: The revenue is R(x) = px, and the profit is P(x) = R(x) – C(x). - Find the revenue function, R(x) = px. R(x) = Find the profit function, P(x) = R(x) — C(x). P(x) = = Find the derivative of the profit function, P(x). P'(x) = = Find the critical number of the function P(x). (Round your answer to the nearest whole number.) X = To maximize its profits, how many copies should Phonola produce each month? (Round your answer to the nearest whole number.) discs/month
Transcribed Image Text:The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, produced by Phonola Media, is related to the price per compact disc. The equation p = 0.00038x + 7 (0 ≤ x ≤ 12,000) where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by C(x) = 600 + 2x 0.00001x² (0 ≤ x ≤ 20,000). Hint: The revenue is R(x) = px, and the profit is P(x) = R(x) – C(x). - Find the revenue function, R(x) = px. R(x) = Find the profit function, P(x) = R(x) — C(x). P(x) = = Find the derivative of the profit function, P(x). P'(x) = = Find the critical number of the function P(x). (Round your answer to the nearest whole number.) X = To maximize its profits, how many copies should Phonola produce each month? (Round your answer to the nearest whole number.) discs/month
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