A hotel has 200 rooms and 2 fares: low fare, which is $250 per night's stay, and high fare, which is $350 per night's stay. The low fare is for leisure travelers who will book first, and the high fare is for business travelers who will book after all leisure travelers have made their booking. Suppose that there are a sufficiently large number of leisure travelers, which means that every room except rooms kept for business travelers will be booked by leisure travelers. If a low-fare room is booked, the hotel will spend $14 in hiring a part-time employee to clean the room ($14/room); if a high-fare room is booked, the hotel will spend $25 in hiring a part-time employee to clean the room thoroughly ($25/room). For both types of rooms, if they are booked, the hotel has to pay $10/room for the consumption of electricity and water. The number of business travelers who want to book a room is discrete uniformly distributed over 41, 42, ..., 50.

Please find out the optimal protection level for the high fare (i.e., the number of rooms reserved for business travelers to book) that maximizes the expected total profit of the hotel. (Please show your calculation)