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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Mathematics

8 July, 23:57

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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Leslie James · 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.