Question 1: A competing hotel has 150 rooms with standard Queen-size beds and two rates: a full price of $200 and a discount price of $120. To receive the discount price, a customer must purchase the room at least two weeks in advance (this helps to distinguish between leisure travelers, who tend to book early, and business travelers who value the flexibility of booking late). You may assume that if a leisure traveler is not able to get the discount rate, she will choose to book at another hotel.

For a particular Tuesday night, the hotel estimates that the average demand by business travelers has a mean of 70 rooms and a standard deviation of 29 rooms. Assume that demand follows a Normal distribution around the forecast.

a. Find the optimal protection level for full price rooms (the number of rooms to be protected from sale at a discount price).

  b. Find the booking limit for discount rooms.

 c. Suppose that for a short time, the hotel's forecast of business customer demand is biased upward: the forecast of 70 rooms is too high and fewer business customers appear, on average. Qualitatively describe the economic consequences of using the protection level and booking limit derived in (a) and (b).

d. Suppose that for a short time, the hotel's forecast of business customer demand is biased downward: the forecast of 70 rooms is too low and more business customers appear, on average. Qualitatively describe the economic consequences of using the protection level and booking limit derived in (a) and (b).

Question 2: An airline offers two fare classes for coach seats on a particular flight: full-fare class at $440/ticket and economy class at $218/ticket. There are 230 coach seats on the aircraft. Demand for full-fare seats has a mean of 43, a standard deviation of 8, and the following empirical distribution:

 Economy-class customers must buy their tickets three weeks in advance, and these tickets are expected to sell out.

a) Find the (i) protection level and (ii) booking limit for low-fare seats.

b) Suppose that unsold seats may sometimes be sold at the last minute at a very reduced rate (similar to USAirways' "esavers" for last-minute travel). What effect will this have on the protection level calculated in (a)? Explain.

Question 3: An aircraft has 100 seats, and there are two types of fares: full ($499) and discount ($99).

a) While there is unlimited demand for discount fares, demand for full fares is estimated to be Poisson with mean l=20 (the table below gives the distribution function). How many seats should be protected for full-fare passengers?

  b) An airline has found that the number of people who purchased tickets and did not show up for a flight is normally distributed with mean of 20 and standard deviation of 10. The airline estimates that the ill will and penalty costs associated with not being able to board a passenger holding confirmed reservation are estimated to be $600. Assume that opportunity cost of flying an empty seat is $99 (price that discount passenger would pay). How much should airline overbook the flight?