In: Statistics and Probability
Round Tree Manor is a hotel that provides two types of rooms
with three rental classes:...
Round Tree Manor is a hotel that provides two types of rooms
with three rental classes: Super Saver, Deluxe, and Business. The
profit per night for each type of room and rental class is as
follows:
|
|
Rental Class |
|
|
Super Saver |
Deluxe |
Business |
Room |
Type I (Mountain View) |
$35 |
$40 |
- |
Type II (Street View) |
$25 |
$35 |
$45 |
Round Tree's management makes a forecast of the demand by rental
class for each night in the future. A linear programming model
developed to maximize profit is used to determine how many
reservations to accept for each rental class. The demand forecast
for a particular night is 150 rentals in the Super Saver class, 55
in the Deluxe class, and 40 in the Business class. Since these are
the forecasted demands, Round Tree will take no more than these
amounts of each reservation for each rental class. Round Tree has a
limited number of each type of room. There are 100 Type I rooms and
110 Type II rooms.
(a) |
Formulate and solve a linear program to determine how many
reservations to accept in each rental class and how the
reservations should be allocated to room types. If an amount is
zero, enter “0”. |
|
Rental Class with room type |
No of Reservations |
Super Saver rentals allocated to room type I |
|
Super Saver rentals allocated to room type II |
|
Deluxe rentals allocated to room type I |
|
Deluxe rentals allocated to room type II |
|
Business rentals allocated to room type II |
|
|
|
|
(b) |
For the solution in part (a), how many reservations can be
accommodated in each rental class? |
|
Rental Class |
No of Reservations |
Super Saver I |
|
Deluxe |
|
Business |
|
|
|
|
|
Demand for - Select your answer -Deluxe / Super Saver /
Business rental class was not satisfied. |
|
|
(c) |
With a little work, an unused office area could be converted to
a rental room. If the conversion cost is the same for both types of
rooms, would you recommend converting the office to a Type I or a
Type II room? |
|
|
Type I |
Type II |
Shadow Price |
$ |
$ |
|
|
|
|
Convert an unused office area to - Select your answer
-Type I / Type II 12 room. |
|
|
|
Explain. |
|
The input in the box below will not be graded, but may be
reviewed and considered by your instructor. |
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(d) |
Could the linear programming model be modified to plan for the
allocation of rental demand for the next night? |
|
- Select your answer -Yes/No |
|
|
|
What information would be needed and how would the model
change? Explain. |
|
The input in the box below will not be graded, but may be
reviewed and considered by your instructor. |
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