Question $2.$ De Pijp Hotel has $300$ rooms used by both business and leisure travelers. It is now the end of April, and the hotel is beginning to take reservations for August. Full price for a room is $$150$ per night. The hotel managers are interested in overbooking analysis as there is a chance that a customer with a reservation may not appear. The hotel receives no revenue from a customer who does not show up$.$ The hotel receives half of the room price from a customer who "bumps", and arranges an alternative accommodation for these customers in NearHotel whose room price is $$350$ per day.

i$)(5$ pts$)$ Find the cost of overbooking $($co$)$ and underbooking $(cu).$

ii$)$ How many rooms should De Pijp Hotel overbook, if the number of customers who book a room but fail to show up on the night has;

a$)(5$ pts$)$ Normal distribution with mean $30$ and standard deviation $9.$

b$)(10$ pts$)$ Poisson distribution with mean rate $28.$ PART B SHOULD BE IN EXCEL FORMAT