Question

Maximizing Profits 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 = -0.00035x + 7 (0 SX s 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 sxs 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.) 4878 discs/month

Answer 1

Q. Þ= -0.00035 x +7 0<x<12000 þ denotes the unit price in dollars 4x is no of discs Total monthly cost for pressing and Packaging. x copies C(x) = 600 +2% -0.00003 x2 0<x< 20,000 Now Revenue R(x) = px RC)= (-0.000352 +7)x -0.0003 582 +72 then Profit PQ) = R(X) –C(X) P(x) = (-0 000 35x37x)-(460 - 93 - 0:00003x) P(x) = -0.000 32x2 +5X-600 defferentiating wr+x d P(x) da for maximising the profit d P(x) = 0 (-0.00032) 2x +5 = 0 + .00064 X 5= 64 100000 5x100000 69 x= 78 12.5 so no. of discs must be around 7812 approx. for maximising the profit = 0.00032) x2x +5. x= 2020-6-15 07:22