A theater finds that there is a correlation between the number of ice cream flavors offered at its food stand and the number of tickets they sell for a show, which can be modeled by the function
S(n) = - 5n^2+ 280n + 5 where n is the number
of ice cream flavors and S(n) is the number of tickets sold.
a) What number of ice cream flavors should be available in order to maximize the number of tickets sold? Show your work.
b) If the tickets are sold for $30 each, what is the maximum ticket revenue the theater can make on a given night?