Hotel XYZ has noticed that weekdays are often fully booked, and that weekday demand sometimes exceeds room supply. Currently, Hotel XYZ charges $300 per room per night. (All rooms at the hotel are comparable, so the price is the same for all rooms.) Demand for $300 rooms is robust, and Hotel XYZ generally fills all its rooms. Based on market research, Hotel XYZ estimates that business travelers are willing to pay $375 per room per night. Hotel XYZ would like to raise its room price. However, business traveler demand on any given weekday evening is equally likely to be between 125 and 175 (inclusive of 175, and exclusive of 125; that is, in the set {126,127,128,...,175})- not enough to occupy all rooms. Furthermore, business travelers tend to book at the last minute, meaning that Hotel XYZ cannot count on first offering rooms at $375, and second lowering its price to $300 to fill all its rooms. Hotel XYZ decides on the following pricing plan. Hotel XYZ will offer rooms at the $300 price until n rooms are booked, and then will raise its price to $375 to try to capture last minute business travel demand. What should n be in