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 organization$$s 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.

$$Any reservation that is not honored by the hotel will cost the hotel $$256.$ The $$256$ 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.

Complete the table below to help you solve this problem.

Row $1$ Number who show up $23242526$

Row $2$ probability $0\mathrm{.}30\mathrm{.}40\mathrm{.}20\mathrm{.}1$

Row $3$ revenue

Row $4$ variable cost

Row $5$ fixed cost

Row $6$ profit $=$ revenue $-$ variable cost $-$ fixed cost

What is the Expected Daily Profit for this hotel. Report your answer with at least $1$ decimal place.