5. Overbooking in the Hospitality Industry. A small hotel has 50 rooms that rent for $105 per night and cost $45 to clean and prepare each night they are used. All rentals are by reservation and there is a 10 percent chance that an individual reservation will not show up. If a customer arrives at the hotel with a reservation and there is no room available due to overbooking, the hotel will rebate the cost of the room and pay on average $150 to put the customer up at another hotel. The hotel would like to determine its overbooking limit: the number of rooms to accept reservations for each night in excess of capacity. Its objective is to maximize expected profits. * What is the expected profit with an overbooking limit of 50? * What is the optimal overbooking limit? * Using the optimal overbooking limit, what is the expected number of customers turned away? * How sensitive is the optimal overbooking limit to rental prices in the range from $90 to $125 per night?