Hilton on Time Square, New York City, has 444 guest rooms. Hilton can sell all its hotel rooms at a discounted price of $260 per night to customers with a two-week advanced purchase. Hilton can also sell its hotel rooms at its full price of $380 per night to customers without advanced purchase. For any unsold hotel room, Hilton has a 75% chance of selling it to some bidder from priceline.com at $120 per night on the day before. The number of customers who buy at full price without advanced purchase can be 100, 200, 300, or 400, with equal probability. Answer the following questions.

1. What is the overage cost of a full-price room?

2. What is the underage cost of a full-price room?

3. How many rooms should Hilton reserve for the customers without advanced purchase?

4. What is the probability all full-price customers will get a room?

5. What is the expected fraction of full-price customers who get a room?

6. What are the number of expected sales of full-fare customers?

7. What is the number of expected sales of discounted customers?

8. What is the number of expected sales from priceline customers?

9. What is Hilton's expected revenue?