Q3 Question #3 The manager of the Midtown hotel is in the process of redesigning the company's reservation system. The hotel has 300 rooms divided into 200 regular double-bed rooms and 100 luxury rooms. The prices for double and luxury rooms are $150 and $250 per night, respectively. The manager wants the new reservation system to be able to handle upgrades. Specifically, if at some point in time all double-bed rooms are booked for a given night and there are still enough luxury rooms available for that same night then an incoming request for a double should be upgraded to a luxury at no extra charge instead of being rejected. A. Suppose that on December 28th all double rooms are booked for the night of New Year's Eve and there are still 40 luxury rooms available. How many more double-room requests should the reservation system accept (using the upgrade option) before start rejecting them? Assume that the (aggregate) demand for luxury rooms in the next three days for the night of New Year's Eve is normally distributed with mean 25 rooms and standard deviation 10 rooms. Assume ample demand for double rooms B. What is the expected number of luxury rooms that the hotel will book at the full rate $250 on New Year Eve using the strategy in part (a)? What is the total expected revenue that the hotel will make that night? C. The manager is contemplating an alternative type of upgrade that works as follows. If all double rooms are booked and there is a new request for a double, the reservation system offers this new customer a luxury room for $150 but with the restriction that the hotel is allowed to cancel this reservation at the last-minute reimbursing the customer $200 ($150 for the room plus $50 as a compensation fee). Under the same conditions of part (a), how many upgrades should the reservation system accept?