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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 follow Room Max Type I Type II s.t. Demand for Super Saver Demand for Deluxe Demand for Business Type I Rooms Type II Rooms Super Saver $30 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 160 rentals in the Super Saver class, 70 rentals in the Deluxe class, and 60 rentals 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. D.D. 8. 20 Rental Class $20 (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. (Assume S₁ is the number of Super Saver rentals allocated to room type 1, S₂ Is the number of Super Saver rentals allocated to room type II, D, is the number of Deluxe rentals allocated to room type 1, D₂ Is the number of Deluxe rentals allocated to room type II, B, is the number of Business rentals allocated to room type II. Write your answers expressing the amount allocated in dollars.) Deluxe $35 $30 Business $40

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 follow Room Max Type I Type II s.t. Demand for Super Saver Demand for Deluxe Demand for Business Type I Rooms Type II Rooms Super Saver $30 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 160 rentals in the Super Saver class, 70 rentals in the Deluxe class, and 60 rentals 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. D.D. 8. 20 Rental Class $20 (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. (Assume S₁ is the number of Super Saver rentals allocated to room type 1, S₂ Is the number of Super Saver rentals allocated to room type II, D, is the number of Deluxe rentals allocated to room type 1, D₂ Is the number of Deluxe rentals allocated to room type II, B, is the number of Business rentals allocated to room type II. Write your answers expressing the amount allocated in dollars.) Deluxe $35 $30 Business $40

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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S1, S2, D₁, D₂, B₂ 20 Report the number of reservations of each type management should accept for each rental class room type combination to maximize profit. Room Type I $ Type II Super Saver Rental Class Deluxe What is the profit (in dollars) obtained through this allocation of room reservations. -Select-- Business (b) For the solution in part (a), how many reservations can be accommodated In each rental class? Super Saver Deluxe Business Is the demand for any rental class not satisfied? If demand materializes as forecast, there will be rooms not reserved in the ---Select-- ✓ class. (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? Why? because this will increase 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? O 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. O 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. O 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. O We would need to know whether the profit per night of each type of room and rental class will change and modify all the constraints appropriately.
Transcribed Image Text:S1, S2, D₁, D₂, B₂ 20 Report the number of reservations of each type management should accept for each rental class room type combination to maximize profit. Room Type I $ Type II Super Saver Rental Class Deluxe What is the profit (in dollars) obtained through this allocation of room reservations. -Select-- Business (b) For the solution in part (a), how many reservations can be accommodated In each rental class? Super Saver Deluxe Business Is the demand for any rental class not satisfied? If demand materializes as forecast, there will be rooms not reserved in the ---Select-- ✓ class. (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? Why? because this will increase 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? O 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. O 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. O 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. O We would need to know whether the profit per night of each type of room and rental class will change and modify all the constraints appropriately.
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 Max Type I Type II s.t. Demand for Super Saver Demand for Deluxe Demand for Business Type I Rooms Type II Rooms S₁, S₂ Super Saver $30 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 160 rentals in the Super Saver class, 70 rentals in the Deluxe class, and 60 rentals 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. B, 20 Rental Class $20 (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. (Assume S₁ is the number of Super Saver rentals allocated to room type I, S₂ Is the number of Super Saver rentals allocated to room type II, D₁ Is the number of Deluxe rentals allocated to room type I, D₂ Is the number of Deluxe rentals allocated to room type II, B₂ is the number of Business rentals allocated to room type II. Write your answers expressing the amount allocated in dollars.) Deluxe $35 $30 00000 Business $40
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 Max Type I Type II s.t. Demand for Super Saver Demand for Deluxe Demand for Business Type I Rooms Type II Rooms S₁, S₂ Super Saver $30 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 160 rentals in the Super Saver class, 70 rentals in the Deluxe class, and 60 rentals 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. B, 20 Rental Class $20 (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. (Assume S₁ is the number of Super Saver rentals allocated to room type I, S₂ Is the number of Super Saver rentals allocated to room type II, D₁ Is the number of Deluxe rentals allocated to room type I, D₂ Is the number of Deluxe rentals allocated to room type II, B₂ is the number of Business rentals allocated to room type II. Write your answers expressing the amount allocated in dollars.) Deluxe $35 $30 00000 Business $40
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