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# Hilton Inn Probability and Inventory Control for Overbooking

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The Hilton Inn has decided to use good inventory control to decide how many customers to book to the hotel. The hotel has 100 rooms and Hilton Inn charges \$120 per night per room. The number of no-shows has the following probability distribution:

Number of no shows Probability
0 0.10
1 0.15
2 0.20
3 0.15
4 0.10
5 0.05
6 0.05
7 0.05
8 0.05
9 0.05
10 0.05

If Hilton Inn overbooks and no room is available, the customer is sent to the Sheraton across the street and the Hilton Inn customers, seeing that this is a nicer hotel, accept this without any protest or requesting any further compensation. Hilton Inn pays the Sheraton \$170 for each room they use in an overbooking situation (but keeps the \$120 they got from the customer).

Under the above described scenario, how many rooms should Hilton Inn overbook?