Question

The Days Inn hotel has 30 rooms with standard queen-size beds and two rates: a full price of $219 and a discount price of $129. To receive the discount price, a customer must purchase the room at least one week in advance (this helps to distinguish between leisure travelers, who tend to book early, and business travelers, who value the flexibility of booking late). For a particular Monday night, the hotel estimates that the demand from leisure travelers could fill the whole hotel while the demand from business travelers is distributed according to Poisson distribution with mean 8.5 (see table below). Q F(Q) Q F(Q) 0 0.0002 10 0.7634 1 0.0019 11 0.8487 2 0.0093 12 0.9091 3 0.0301 13 0.9486 4 0.0744 14 0.9726 5 0.1496 15 0.9862 6 0.2562 16 0.9934 7 0.3856 17 0.9970 8 0.5231 18 0.9987 9 0.6530 19 0.9995 (a) Find the optimal protection level for full-price rooms for the particular Monday night. Given the optimal protection level for full-price rooms computed in (a), the manager computes that the expected number of business travelers that will be denied is 3. Answer the following questions. (b) Given the optimal protection level for full-price rooms computed in (a), what is the expected total revenue from the full price rooms on the particular Monday night? (c) Given the optimal protection level for full-price rooms computed in (a), what is the expected total revenue of the hotel on the particular Monday night? (d) Given the optimal protection level for full-price rooms computed in (a), what is the expected number of occupied rooms (occupancy rate) on the particular Monday night? (e) Suppose the Inn can observe all business demands one day in advance (say, the Inn can observe next Monday night demand of business travelers on this Sunday). With this capability, the Days Inn can sell all its empty rooms (which were protected for business travelers but left unoccupied) through "priceline.com" at a discount price of $109. In this new situation, what is the optimal protection level for full-price rooms for the Monday night? (f) Why has the protection level in (e) changed compared to your answer in (a)?

          The Days Inn hotel has 30 rooms with standard queen-size beds and two rates: a full price of $219 and a discount price of $129. To receive the discount price, a customer must purchase the room at least one week in advance (this helps to distinguish between leisure travelers, who tend to book early, and business travelers, who value the flexibility of booking late). For a particular Monday night, the hotel estimates that the demand from leisure travelers could fill the whole hotel while the demand from business travelers is distributed according to Poisson distribution with mean 8.5 (see table below).
Q F(Q) Q F(Q)
0 0.0002 10 0.7634
1 0.0019 11 0.8487
2 0.0093 12 0.9091
3 0.0301 13 0.9486
4 0.0744 14 0.9726
5 0.1496 15 0.9862
6 0.2562 16 0.9934
7 0.3856 17 0.9970
8 0.5231 18 0.9987
9 0.6530 19 0.9995
(a) Find the optimal protection level for full-price rooms for the particular Monday night.

Given the optimal protection level for full-price rooms computed in (a), the manager computes that the expected number of business travelers that will be denied is 3. Answer the following questions.

(b) Given the optimal protection level for full-price rooms computed in (a), what is the expected total revenue from the full price rooms on the particular Monday night?
(c) Given the optimal protection level for full-price rooms computed in (a), what is the expected total revenue of the hotel on the particular Monday night?
(d) Given the optimal protection level for full-price rooms computed in (a), what is the expected number of occupied rooms (occupancy rate) on the particular Monday night?

(e) Suppose the Inn can observe all business demands one day in advance (say, the Inn can observe next Monday night demand of business travelers on this Sunday). With this capability, the Days Inn can sell all its empty rooms (which were protected for business travelers but left unoccupied) through "priceline.com" at a discount price of $109. In this new situation, what is the optimal protection level for full-price rooms for the Monday night?
(f) Why has the protection level in (e) changed compared to your answer in (a)?

The Days Inn hotel has 30 rooms with standard queen-size beds and two rates: a full price of 219 and a discount price of129. To receive the discount price, a customer must purchase the room at least one week in advance (this helps to distinguish between leisure travelers, who tend to book early, and business travelers, who value the flexibility of booking late). For a particular Monday night, the hotel estimates that the demand from leisure travelers could fill the whole hotel while the demand from business travelers is distributed according to Poisson distribution with mean 8.5 (see table below).
Q F(Q) Q F(Q)
0 0.0002 10 0.7634
1 0.0019 11 0.8487
2 0.0093 12 0.9091
3 0.0301 13 0.9486
4 0.0744 14 0.9726
5 0.1496 15 0.9862
6 0.2562 16 0.9934
7 0.3856 17 0.9970
8 0.5231 18 0.9987
9 0.6530 19 0.9995
(a) Find the optimal protection level for full-price rooms for the particular Monday night.

Given the optimal protection level for full-price rooms computed in (a), the manager computes that the expected number of business travelers that will be denied is 3. Answer the following questions.

(b) Given the optimal protection level for full-price rooms computed in (a), what is the expected total revenue from the full price rooms on the particular Monday night?
(c) Given the optimal protection level for full-price rooms computed in (a), what is the expected total revenue of the hotel on the particular Monday night?
(d) Given the optimal protection level for full-price rooms computed in (a), what is the expected number of occupied rooms (occupancy rate) on the particular Monday night?

(e) Suppose the Inn can observe all business demands one day in advance (say, the Inn can observe next Monday night demand of business travelers on this Sunday). With this capability, the Days Inn can sell all its empty rooms (which were protected for business travelers but left unoccupied) through "priceline.com" at a discount price of 109. In this new situation, what is the optimal protection level for full-price rooms for the Monday night?
(f) Why has the protection level in (e) changed compared to your answer in (a)?

Added by Johnny M.

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