You operate a rental car company where you offer two rates for customers. You charge any customers who reserve a car at least one week in advance, a flat rate of $180 to rent a car for the weekend. Any customers who place their reservation within one week of the rental period are charged a higher, “close-in” reservation price of $300 to rent a car for the weekend. You have 50 identical cars available for rental. You estimate that the number of customers who will place their reservation late (i.e. within one week of the rental) is uniformly distributed between 4 and 15.

a) Youhavealreadyacceptedreservationsfor40carrentalsduringtheweekend of May 28th. You have the ability to close the reservation portal and prevent more customers from placing reservations until the week before May 28th. You are certain that if you do not close the portal, you will completely book all 50 rental cars at the normal low price of $180. If your goal is to maximize expected revenue, should you keep accepting reservations at the normal price or should you close the portal and reserve the remaining cars for “close-in” reservations?

Keep accepting normal price reservations

b) In general, how many cars should you save for “close-in” reservations?

Save 8 cars for close-in reservations

c) What is the expected number of“close-in”bookings placed for the weekend of May 28th if you follow the strategy from part b)?