math
posted by Teetee (Please Help) on .
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+2x0.00004x^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

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.