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 = −0.00042x + 5 (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 − 0.00004x2 (0 ≤ x ≤ 20,000). To maximize its profits, how many copies should Phonola produce each 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 = −0.00042x + 5 (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 − 0.00004x2 (0 ≤ x ≤ 20,000). To maximize its profits, how many copies should Phonola produce each month?
Chapter1: Equations, Inequalities, And Mathematical Modeling
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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 = −0.00042x + 5 (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 − 0.00004x2 (0 ≤ x ≤ 20,000).
To maximize its profits, how many copies should Phonola produce each month?
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