A baseball team plays in a stadium that holds 51,000 spectators. With the ticket price at $10, the average attendance at recent games has been 33,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000.
(a) Find a function that models the revenue in terms of ticket price. (Let x represent the price of a ticket and R represent the revenue.)
(b) Find the price that maximizes revenue from ticket sales.
(c) What ticket price is so high that no revenue is generated?