Q$1.(10$ points$)$ Town and Country Rental Car has experienced a substantial increase in business

volume because of recent fare wars between the major air carriers. Town and Country operate 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. Midsize$-$car

customers do not choose to rent a compact when no midsize car is available, or the other way

around. The discount rate is available to persons who are willing to reserve a car in advance, and

there is sufficient demand for the discount rate. The daily demand $($of full rate customers$)$

appears to follow a uniform distribution. 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. Using revenue management, determine the optimal number of compact

and midsize cars to be held for customers paying the full rate. $($SOLVE USING REVENUE MANAGEMENT$)$