Overbooking hotel rooms (Occupancy Management). The practice of overbooking hotel rooms - accepting reservations for more rooms than are available by forecasting the number of no-show reservations with the goal of attaining 100% occupancy - is viewed by the general public with skepticism. Hoteliers and front office managers who practice overbooking do so to meet an organizations financial objectives, i.e. to maximize profits. Assume you are a front office manager for a hotel with 25 rooms, and you are responsible for administering and developing a policy on overbooking. In this hotel we will assume that all reservations are Guaranteed reservations where prospective guests have made a contract with the hotel for a room. Below are a few facts to help with the problem.

The hotel has a maximum capacity of 25 rooms. The hotel makes revenue of $100 for each room that is occupied (If a customer cancels or is denied a room the hotel does not get any money from this customer). The hotel has a policy to make exactly 26 Guaranteed reservations each day. Any reservation that is not honored by the hotel will cost the hotel $300. The $300 is the cost to pay for a nearby hotel room and provide the customer with a complementary dinner at a nearby restaurant. Assume that the hotel has a fixed daily operating cost of $1,800 and a variable room cleaning and maintenance cost of $20 per occupied room.

Number who show up	23	24	25	26
probability	0.3	0.4	0.2	0.1
revenue
variable cost
fixed cost
profit = revenue - variable cost - fixed cost

What is the Expected Daily Profit for this hotel.