The owner of a video store has determined that the profits "P" of the store are approximately given by P (x) = - x^ (2) + 30x+76, where x is the number of videos rented daily. Find the number of videos that must be rented to get the maximum daily profit, then find the maximum daily profit to the nearest dollar.

Question

Mathematics

Rocco Villegas

19 November, 16:25

The owner of a video store has determined that the profits "P" of the store are approximately given by P (x) = - x^ (2) + 30x+76, where x is the number of videos rented daily. Find the number of videos that must be rented to get the maximum daily profit, then find the maximum daily profit to the nearest dollar.

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Beau Berry · Answer 1

P (x) = - x^2 + 30x + 76

For maximum profit, dP/dt = 0

-2x + 30 = 0

2x = 30

x = 30/2 = 15

The number of videos that must be rented to get the maximum daily profit is 15.

The maximum profit = - (15) ^2 + 30 (15) + 76 = - 225 + 450 + 76 = $301.