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 p = - 0.00054x + 9 (0 ≤ x ≤ 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 - 0.00002x2 (0 ≤ x ≤ 20,000)

Question

Cha Cha

Mathematics

22 July, 02:23

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 p = - 0.00054x + 9 (0 ≤ x ≤ 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 - 0.00002x2 (0 ≤ x ≤ 20,000)

+1

Answers (1)

Know the Answer?

Cayden Schroeder · Answer 1

We can get the Profit function P (x) from the Hint.

the Profit function is: P (x) = xp (x) - C (x) = - 0.00041 x2 + 4x - 600

Attention: don't get confuse by the big P of the profit with the small p of the price To calculate the maximum profit, we need to find the derivative of P (x) then set it to 0 then find x: dP (x) / dx = - 0.00082 x + 4 = 0, so x = 4/0.00082 = 4,878 copies each month.