Problem 6 (10 points) Hilton NY has 100 total rooms available for Jan 22. There are two types of customers, business customers (high fare) and leisure customers (low fare). Hilton charges high fare $300/ night and low fare \$150ight. High fare does not need pre-booking and has time flexibilities; low fare needs pre-booking. Assume business customers always take the high fare option and leisure customers always take the low fare option. Leisure customers always book far earlier before business customers and there are sufficient leisure customers. The total number of business customers is uncertain following the table below. a. How many rooms should Hilton reserve for business customers on Jan 22 ? [6 pts] b. Suppose Hilton reserves 50 rooms for business customer, what is the expected revenue for Hilton on Jan 22? [4 pts]