An important operations decision for service business such as hotels and airlines is the number of reservations to accept to effectively fill capacity knowing that some customers may not use their reservations. If a hotel, for example, holds rooms for customers who do not show up, they lose revenue opportunities. A common practice in these industries is to overbook reservations. When more customers arrive than can be handled, the business usually incurs some cost to satisfy them (by putting them up at another hotel). A popular resort hotel that has 300 rooms charges $120 per room per day. Reservations may be canceled by the 6:00 pm deadline with no penalty. The hotel has estimated that the average overbooking cost is $100. Based on historical data, customer demand can be modeled based on the following discrete distribution: Demand 280 285 290 295 300 305 310 315 320 325 330 335 Probability 0.02 0.03 0.03 0.05 0.08 0.12 0.15 0.20 0.15 0.10 0.05 0.02 The hotel is willing to accept 310 reservations; that is, to overbook by 10 rooms. Also, it is fair to assume that cancellations follow a Normal Distribution with mean and standard deviation equal to 4 and 1, respectively