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Maximizing Profits The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata,...

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Basic Math

Maximizing Profits The quantity demanded each month of theWalter Serkin recording of Beethoven's Moonlight Sonata, producedby Phonola Media, is related to the price per compact disc. Theequation p = −0.00044x + 10 (0 ≤ x ≤ 12,000) where p denotes theunit price in dollars and x is the number of discs demanded,relates the demand to the price. The total monthly cost (indollars) for pressing and packaging x copies of this classicalrecording is given by C(x) = 600 + 2x − 0.00004x2 (0 ≤ x ≤ 20,000).To maximize its profits, how many copies should Phonola produceeach month? Hint: The revenue is R(x) = px, and the profit is P(x)= R(x) − C(x). (Round your answer to the nearest whole number.)discs/month.

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