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.)

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

answer:   14

step-by-step explanation:          

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