An amusement park has estimated the following demand equation for the average park guest

Q=162P

Where Q represents the number of rides per guest and P the price per ride. The total cost of providing rides to a guest is

TC=2+0.5Q

a.) If a one-price policy is used, how much should it charge per ride if the park wishes to maximize its profit?

b.) What is the park's profit for each guest?

c.) If a two-part tariff policy is used, what admission fee should the park charge to maximize its profit?

d.) What is the park's profit for each guest?