Problem 3 (25 points) Your learning team recently invested in a small boutique hotel in Montauk. The hotel has 20 standard rooms. During the peak summer season, the hotel is always sold out on weekends .Yet historically 16% of customers cancel their bookings prior to arrival .While occasionally your hotel can find a last-minute customer to compensate for a cancellation, often the rooms simply go vacant. To hedge against this loss in revenue, you are considering adopting an overbooking policy . But before doing so, however ,your team wants to assess the risk and reward of overbooking (a) Construct a simulation model of the occupancy of your hotel on a peak summer night. Assume you receive 20 reservations, but some of those 20 reservations cancel randomly. The probability that a given reservation cancels is 0.16. Create a spreadsheet model to simulate these cancellations and compute the number of customers who show up on the simulated night . Explain all formulas used in your spreadsheet model . (b) Use your model in part (a) to simulate 1,000 nights of operation of your hotel. What is your estimate of the average occupancy (number of guests staying at the hotel)? What is the probability that the hotel is full '2 Hint: To estimate a probability for a given event, you may simulate whether the event takes place (1) or not (0) on a given sample path , and then estimate the average of that cell (the average fraction of times that a one appears )through Monte -Carlo simulation (c) Now consider overbooking your hotel by one room. That is, suppose you now accept 21 reservations as a hedge against cancellations, knowing that there is some chance a customer might have to be "walked" if all 21 reservations arrive. Simulate 1,000 days of operation of your hotel with this new overbooking policy. What is the average occupancy (number of guests staying at the hotel)? What is the average number of walked customers per night? (d) Repeat your analysis from (:3) when you overbook by 2, 3 and 4. Provide a table of the average occupancy and average number of walked customers each night for each of the four overbooking policies (e) Based on your results, which policy would you adopt? (No right or wrong answer here, but think in terms of what you would choose if this was your hotel and what factors would influence your decision .)