Suppose an amusement park faces the following demand for roller coaster rides: P = 10 Q, where P is the price of a single ride on the roller coaster and Q is the number of rides. The marginal cost per roller coaster ride is $2. The amusement park decides to implement a two-part pricing scheme. They will charge a price per roller coaster ride as well as an entry fee.

(a) What is the profit-maximizing price per rollercoaster ride?

(b) What is the profit-maximizing entry fee?