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 companys 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.

\begin{tabular}{|c|c|c|c|} \hline Car & Full Rate & Discount Rate & \begin{tabular}{c} Daily Demand (on the \\ day of rental) \end{tabular} \\ \hline Compact & $30 & $20 & \begin{tabular}{c} Uniform between \\ {[40,60]} \end{tabular} \\ \hline Midsize & $45 & $30 & \begin{tabular}{c} Uniform between \\ {[25,35]} \end{tabular} \\ \hline \end{tabular}