At a price of $8 per ticket, a theater group can fill every seat in the theater, which has a seating capacityof 990. For every additional dollar charged, the number of people buying tickets decreases by 60.

a. Define a function, R(p), that gives revenue for the performance if a single ticket costs $p.

b. Using R'(p), determine the ticket price that maximizes revenue. Also, compute the maximum possible revenue for the performance.