Concert Tickets: The revenue at the Assembly Center depends on the number of seats sold for the Willie Williams and the Wranglers concert. At $10 per ticket, they will fill all 8000 seats. The manager knows that for every $1 increase in the price, 500 tickets will go unsold. If the revenue in dollars, R(p), is given by R(p) = 500p^2 + 13000p, where p is the price per ticket sold.

(a) What ticket price will produce a maximum revenue? What is the maximum revenue? You must show this algebraically.

(b) Find the number of unsold seats that resulted in this maximum revenue given the following n = 13000 500p where n is the number of seats sold and p is the price. You must show this algebraically