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Rainbow [258]
3 years ago
11

the manager of a symphony computes that the symphony will earn -40p^2+1100p dollars per concert if they charge P dollars for tic

kets. what ticket price should the symphony charge in order to maximize its profits?
Mathematics
1 answer:
cluponka [151]3 years ago
5 0

Answer:

$7,562.5

Step-by-step explanation:

Given the function of the profit earned expressed as;

<em>f(p) =-40p^2+1100p</em>

To maximize the profit, df(p)/dp must be sero

df(p)/dp = -80p + 1100 = 0

-80p + 1100 = 0

-80p = - 1100

p = 1100/80

p = 13.75

Substitute p = 13.75 into the function

f(13.75) =-40(13.75)^2+1100(13.75)

f(13.75) = -7,562.5+15,125

f(13.75) = 7,562.5

Hence the symphony should charge $7,562.5 to maximize the profit.

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