An amusement park has estimated the following demand equation

for the average park guest

Q = 16 - 2P

where Q represents the number or rides per guest, and P the price per ride.

The total cost of providing a ride is characterized by the equation

TC = 2 + 0.5Q

a. How much should the park charge on a per-ride basis to maximize its

profit? What is the amusement park's total profit per customer?