The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, produced by PhonolaMedia, is related to the price per compact disc. The equationp = -0.00041x + 6(0 < x < 12,000)wheredenotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. The totalmonthly cost (in dollars) for pressing and packaging x copies of this classical recording is given byC(x) = 600 + 2x- 0.00004x2(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) = -0.00041x2 + 6xFind the profit function, P(x) = R(x) – C(x).P(x) = -0.00037x² + 4x – 600Find the derivative of the profit function, P(x).P'(x) = -0.00074x + 4%3DFind 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 wholenumber.)discs/month

Name: The quantity demanded each month of the Walter Serkin recording of Be
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, produced by PhonolaMedia, is related to the price per compact disc. The equationp = -0.00041x + 6(0 < x < 12,000)wheredenotes the unit price in dollars