Richardson Hotel recently hired you as an operations manager to help improve its revenues. The hotel has 200 rooms and given its quality and service, the hotel is always able to fill up the rooms with advance reservations. The hotel charges $250 per room per night for advance reservations and stops taking additional reservations once all the 200 rooms have been booked. (a) (7 points) You observe that many of the guests tend to cancel their reservations at the last minute, which results in hotel rooms being unoccupied. You see this as a missed revenue opportunity and decide to implement the practice of overbooking. If a guest shows up and a room is not available, you have to pay the guest $1000 to make alternate arrangements. Suppose the number of cancelations follows a normal distribution with mean 20 and standard deviation 5. How many reservations in total should the hotel take to maximize their expected profit? Probability z 0.2 -0.84 0.25 -0.67 0.8 0.84 Cu = Co = Critical Ratio = Number of reservations = (b) (7 points) You also notice that many customers attempt to make last-minute reservations for hotel rooms, but are unable to do so because all the rooms end up being booked in advance. You decide to reserve some number of rooms for last-minute reservations and charge $400 for these requests. Suppose the demand for last-minute reservations follows a uniform distribution between 10 and 50. How many rooms should you reserve for last-minute reservations?