11.9. Town and Country has experienced a substantial increase in business volume because of recent fare wars between the major air carriers. Town and Country operates a single office at a major international airport, with a fleet of 60 compact and 30 midsize cars. Recent developments have prompted management to rethink the company’s reservation policy. The table below contains data on the rental experience of Town and Country:

The daily demand appears to follow a normal distribution; however, it has been observed that midsize-car customers do not choose to rent a compact when no midsize car is available. The discount rate is available to persons who are willing to reserve a car at least 14 days in advance and agree to pick up that car within 2 hours after their flight arrives.
Otherwise, a nonrefundable deposit against their credit card will be forfeited. The current reservation policy is that 40 compact cars are held for customers who are willing to pay the full rate and 25 midsize cars are held for full rate–paying customers.
Car Rental Rate Discount Rate Daily Demand Standard Deviation Compact $30 $20 50 15 Midsize $40 $30 30 10

a. Using yield management, determine the optimal number of compact and midsize cars to be held for customers paying the full rate.

b. Given your optimal reservation policy determined here, would you consider a fleet expansion?