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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

p=-0.00051x+8 (0¡Üx¡Ü12,000)

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-0.00004x^2 (0¡Üx20,000)

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

  • math -

    so, use the hint:

    R(x) = x*p(x) = -0.00051x^2+8x
    P(x) = R(x) - C(x)
    = 2.04*10^-8 x^4 - .00134x^3 + 15.694x^2 + 4800x

    P'(x) = 0 at x = 9929 or so.

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