Calculus

A movie theater wants to determine the price per ticket that should be charged in order to maximize its
revenue. The theater can accommodate 2000 movie goers per night, but the average attendance is about 1400
people per night. The average ticket price is about $8.00. Market research shows that, for each $0.50
reduction in the ticket price, attendance increases by 250 spectators. What should the theater charge per ticket
in order to sell out every show?

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