The weekly demand for dvds manufactured by a certain media corporation is given by
p = −0.0006x2 + 65
where p denotes the unit price in dollars and x denotes the quantity demanded. the weekly total cost function associated with producing these discs is given by
c(x) = −0.002x2 + 13x + 4000
where c(x) denotes the total cost (in dollars) incurred in pressing x discs. find the production level that will yield a maximum profit for the manufacturer. hint: use the quadratic formula. (round your answer to the nearest integer.)

Let the production level that will yield a maximum profit for the manufacturer be x.
The unit price of the disc is given by p = -0.0006x^2 + 65.
The revenue from selling x discs (R(x)) = px = -0.0006x^3 + 65x

Profit = Revenue - Cost = -0.0006x^3 + 65x - (-0.002x^2 + 13x + 4000) = -0.0006x^3 + 0.002x^2 + 52x - 4000

For maximum profit, dP/dx = 0
-0.0018x^2 + 0.004x + 52 = 0
Using quadratic formular, x = 171

Therefore, the production level that will yield a maximum profit for the manufacturer is 171 discs.

Yup! You can good luck!