Although no-shows are an ever growing issue that can slash 10-20% of revenues from an all-booked day, few hotels actually do charge any fees for them....

Although no-shows are an ever growing issue that can slash 10-20% of revenues from an all-booked day, few hotels actually do charge any fees for them. Instead, just like airlines, many overbook their rooms. This means that they book more rooms than they have, in the effort to reduce the number of empty rooms while at the same time hoping that not all guests show up. Please, describe and explain (i) what and what type of decision variables/parameters should a hotel use/estimate in order to maximize profits and minimize losses. Now, assume that a fully booked hotel faces between 0 and 10 no- shows daily with uniform probability. Assume also that the hotel wants to minimize the total loss of empty rooms ($70 each for cost of opportunity) and overbooked customers ($50 each for loss of goodwill) so that revenues and sales profits are disregarded. Please, (ii) create a spreadsheet table that helps determine the optimal overbooking level for the day. Finally, (iii) change the loss of goodwill estimate so that the optimal solution x∗ increases by two. Provide a mathematical and a managerial explanation for the change.