Carlsbad State Beach has (inverse) daily demand on typical days of P_T = 150 5Q_T where Q is number of vehicles admitted to the beach facilities. On weekends and holidays the demand increases to P_H = 550 5Q_H. The marginal cost of maintaining the facilities is a constant $50 for each vehicle, and managers are required to charge no more than $50 per vehicles (no profits earned). The parking lot has a capacity of 75 spaces. Show your answers graphically.

a.Find the number of vehicles in the parking area on typical day demand. Is the $50 parking fee efficient? Explain.

b. Find the efficient number of vehicles to admit with weekend/holiday demand. What is the efficient price to charge? If the managers must keep price at $50, then what is the demand to get into the parking lot? How many vehicles are admitted? How are parking spaces rationed in this case? Explain.