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) $15 $25 $35 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 140 rentals in the Super Saver class, 65 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 120 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 Deluxe Business Demand for 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 room. Explain. Converting the unused office area to this type of room increases profit by $ . (d) Could the linear programming model be modified to plan for the allocation of rental demand for the next night? What information would be needed and how would the model change? Explain. (i) We would need to know how many rooms of Type I and Type II there will be on the next night to use as the right-hand sides of the last two constraints. (ii) We would need to know whether the profit per night of each type of room and rental class will change and use these as objective coefficients. (iii) We would need to know if Type 1 rooms can be used as Business class rooms the next night and add a variable to the objective function. (iv) We would need a forecast of demand for each rental class on the next night to use as the right-hand sides of the first three constraints

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) $15 $25 $35 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 140 rentals in the Super Saver class, 65 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 120 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 Deluxe Business Demand for 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 room. Explain. Converting the unused office area to this type of room increases profit by $ . (d) Could the linear programming model be modified to plan for the allocation of rental demand for the next night? What information would be needed and how would the model change? Explain. (i) We would need to know how many rooms of Type I and Type II there will be on the next night to use as the right-hand sides of the last two constraints. (ii) We would need to know whether the profit per night of each type of room and rental class will change and use these as objective coefficients. (iii) We would need to know if Type 1 rooms can be used as Business class rooms the next night and add a variable to the objective function. (iv) We would need a forecast of demand for each rental class on the next night to use as the right-hand sides of the first three constraints

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

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)	$15	$25	$35

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 140 rentals in the Super Saver class, 65 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 120 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
Deluxe
Business

Demand for 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 room.

Explain.

Converting the unused office area to this type of room increases profit by $ .

(d)

Could the linear programming model be modified to plan for the allocation of rental demand for the next night?

What information would be needed and how would the model change? Explain.

(i)	We would need to know how many rooms of Type I and Type II there will be on the next night to use as the right-hand sides of the last two constraints.
(ii)	We would need to know whether the profit per night of each type of room and rental class will change and use these as objective coefficients.
(iii)	We would need to know if Type 1 rooms can be used as Business class rooms the next night and add a variable to the objective function.
(iv)	We would need a forecast of demand for each rental class on the next night to use as the right-hand sides of the first three constraints

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