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garri49 [273]
3 years ago
15

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)
Mathematics
1 answer:
Olenka [21]3 years ago
7 0
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 <span>big P of the profit with the small p of the price</span> 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.
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