The Mountain Top Hotel is a luxury hotel in a popular ski resort area. The hotel always is essentially full during winter months, so reservations and payments must be made months in advance for week-long stays from Saturday to Saturday. Reservations can be canceled until a month in advance but are nonrefundable after that. The hotel has 100 rooms and the room charge for a week’s stay is $3,000. Despite this high cost, the hotel’s wealthy customers occasionally will forfeit this money and not show up because their plans have changed. On the average, about 10 percent of the customers with reservations are no-shows, so the hotel’s management wants to do some overbooking. However, it also feels that this should be done cautiously because the consequences of turning away a customer with a reservation would be severe. These consequences include the cost of quickly arranging for alternative housing in an inferior hotel, providing a voucher for a future stay, and the intangible cost of a massive loss of goodwill on the part of the furious customer who is turned away (and surely will tell many wealthy friends about this shabby treatment). Management estimates that the cost that should be imputed to these consequences is $20,000.
Use the overbooking model presented in Sec. 18.8, including the normal approximation for the binomial distribution, to determine how much overbooking the hotel should do.