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 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.)

Answer 1

4878 discs

Step-by-step explanation: INCOMPLETE QUESTION

Two pieces of information are missing.

1.-The equation relating p (price in $ )

2.-The equation for the total monthly cost.

I FOUND FROM GOGLE THAT POSSIBLES EQUATIONS COULD BE

1.-The equation relating p (price in $ )

p (x) = - 0.00051*x + 6

2.-The equation for the total monthly cost.

c(x) = 600 + 2*x -0.0001*x²

IF WE ASSUME THAT TWO EQUATIONS AS THE MISSING INFORMATION

We have

Profit = Income (price of product times number of product) - total monthly cost

Then:

P(x) = x* (- 0.00051*x + 6) - ( 600+ 2*x -0.0001*x²)

P(x) = - 0.00051*x² + 6*x - 600 - 2*x + 0.0001*x²

P(x) = -0.00041*x² + 4*x - 600

Taking derivatives on both sides of the equation.

P´(x) = 2(-0.00041*x) + 4 ⇒ P´(x) = 0

2(-0.00041*x) + 4 = 0 ⇒ -0.00082*x = - 4

x = 4 /0.00082

x = 4878