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 Record Industries, is related to the price/compact disc. The equation

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

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

P(x) = R(x)-C(x) = px - C(x) =

x(10 - 0.00047x) - (600 + 2x - 0.00003x2)

We want to find maximum of P(x):

P'(x) = 10 - 0.00094x - 2 + 0.00006x = 0

x = 100000/11 9091 disc/month

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