l. Overbooking hotel rooms (Occupancy Management). The practice of overtooking hotel rooms accepting reservations for more rooms than are available by forecasting the number of noshow reservations with the goal of attaining 100% occupancy is viewed by the general public with skepticism. Hoteliers and front oice managers who practice overbooking do so to meet an organization's nancial objectives, ie. to maximize prots. Assume you are a front ofce manager for a hotel with 25 rooms, and you are responsible for administering and developing a policy on overbooking. In this hotel we will assume that all reservations are Guaranteed reservations where prospective guests have made a contract with the hotel for a room. Below are a few facts to help with the problem. The hotel has a maximum capacity of 25 rooms. The hotel makes revenue of $100 for each room that is occupied (If a customer cancels or is denied a room the hotel does not get any money from this customer). The hotel has a policy to make exactly 26 Guaranteed reservations each day. Any reservation that is not honored by the hotel will cost the hotel $200. The $200 is the cost to pay for a nearby hotel room and provide the customer with a complementary dinner at a nearby restaurant. Assume that the hotel has a xed daily operating cost of $1,600 and a variable room cleaning and maintenance cost of $20 per occupied room. Below is a table for the probability distribution for X (the number of customers who show up at the hotel expecting a room). (a) (b) (C) Number who show up 24 25 26 probability . 0.3 0.25 0.2 revenue variable cost prot = revenue variable cost xed cost What is the probability the hotel has enough rooms for all the customers who arrive at the hotel? What is the expected number of customers who arrive at the hotel? Fill in the table above to help with part (10) to nd the probability distribution for the prot under the three scenarios. Use this to help you nd the expected prot for one operating day assuming the hotel makes 26 guaranteed reservations. HINT: When they make 26 reservations this does not necessarily imply that 26 people show up