Problem 3: Revenue Management You are in charge of the revenue management department at the Richardson's Spa and Boutique Hotel, which has a total of 10 rooms. From previous experience, you know that many guests cancel their reservations at the last minute, which results in hotel rooms being unoccupied. You see this as a missed revenue opportunity, so you decide to implement two changes: (1) a non-refundable fee of $50 per room at the moment of reservation, and (2) overbooking. The price of each room is $200 ($50 from the non- refundable fee + $150 paid at check-in), and if a guest shows up and a room is not available, you have to book a room at the nearby hotel that costs you $500. Based on historical information, you know that cancellations are distributed as summarized in the next table. Number of late Probability Cumulative Probability cancellations 0 0.1 I 0.2 2 0.4 3 0.15 4 0.1 5 0.05 a. (7 points) How many overbookings should you accept? After a couple of bad experiences, you decide to stop overbooking. Instead, you realize that you could also charge $500 for last minute reservations (same as the nearby hotel), and potentially make a higher profit. You don't know what the exact demand from last minute travelers is, but you know that demand is normally distributed with mean 3 and standard deviation 1 for a hotel like yours. b. (7 points) How many rooms should you keep for last minute travelers? In a bold move, you decide to convert some rooms into premium ones, and you must decide how much to charge for each type of room (basic and premium). To make this decision, you surveyed 10 customers and asked them about their willingness to pay. The results of your survey are sununarized in the next table. Willingness to Pay Customer ID Basic Premium NH $200 $500 $300 $600 To keep customers coming, you know that the basic price should be either $100 or $200, while the premium room should be either $300, $400 or $500. In addition, you know that if a customer is indifferent between basic and premium, they choose each option with equal probability. Finally, you also know that if a customer is indifferent between not booking and. booking, they will book for sure. 3 $200 $200 4 $300 $300 5 $400 $700 6 $100 $200 | 7 $300 $300 I 3 $200 $500 I 9 $100 $400 | 10 $300 $500 C. What is the optimal combination of prices to maximize the expected prot obtained from these 10 customers? (Hint: you may want to use Excel)