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 + 8 (0 sxS 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 - 0.00003x? (0 sxS 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) =
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 + 8 (0 sxS 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 - 0.00003x? (0 sxS 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) =
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter3: Math Models
Section3.3: Solve Mixture Applications
Problem 3.58TI: At the movie theater, the total value of tickets sold was $2,612.50. Adult tickets sold for $10 each...
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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 + 8
(0 SxS 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- 0.00003x (0 sxS 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.)
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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