The Overlook Hotel has a problem of guests not showing up. For each no-show the hotel foregoes revenues of $400 on average, though some of it is recuperated through average cost savings of $50 (cleaning and other services). This is especially problematic if the hotel is fully booked and they have to turn down requests. For this reason they are consider to overbook to compensate for the expected no-shows. In case of actual overbookings they plan to re-locate the overbooked guests to the nearby Great Northern Hotel, which will incur an expense of $600 per guest. Frequency of no-shows: Frequency of 1 no-shows = 150 Frequency of 2 no-shows = 100 Frequency of 3 no-shows = 75 Frequency of 4 no shows = 25 Based on this information, what is the optimal number of preliminary overbookings and how large savings could be expected for a given day?