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: Type I (Mountain View) Room Type II (Street View) Rental Class Super Saver Deluxe Business $40 $35 $35 $25 $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 rooms. Deluxe (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 Business 95 65 50 95 X 0 5 (b) For the solution in part (a), how many reservations can be accommodated in each rental class? Rental Class No. of Reservations Super Saver 60 50 X * X
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: Type I (Mountain View) Room Type II (Street View) Rental Class Super Saver Deluxe Business $40 $35 $35 $25 $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 rooms. Deluxe (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 Business 95 65 50 95 X 0 5 (b) For the solution in part (a), how many reservations can be accommodated in each rental class? Rental Class No. of Reservations Super Saver 60 50 X * X
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section: Chapter Questions
Problem 59P
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Transcribed Image Text: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:
Room
Type I (Mountain View)
Type II (Street View)
Rental Class
Super Saver Deluxe Business
$40
$35
$35
$25
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.
Super Saver
(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
Deluxe
Business
95
$45
65
(b) For the solution in part (a), how many reservations can be accommodated in each rental class?
Rental Class
No. of Reservations
50
X
95
0
5
60
50
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