The quantity demanded each month of the Walter Serkin recording of Beethoven\'s

Question

The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, manufactured by Phonola Media, is related to the price per compact disc. The equation

p = ?0.00054x + 10    (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 ? 0.00003x2    (0 ? x ? 20,000)

To maximize its profits, how many copies should Phonola produce each 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

Explanation / Answer

Price-Cost=Profit

-.00042x + 7.6 -600 -2x +.00002x^2 = Profit
.00002x^2 - 2.0042x -592.4 = P

dx/dp derivative and solve for 0

.0004X - 2.0042 = 0
.0004x = 2.0042
X = 5010

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