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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 follows: Room Type I Type II Super Saver $30 Rental Class $20 Deluxe $35 $30 Business $40 Type I rooms do not have high-speed Internet access and are not available for the Business rental class. 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, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. (a) Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Is the demand by any rental class not satisfied? Explain. If demand materializes as forecast, there will be rooms not reserved in the Super Saver class. (b) How many reservations can be accommodated in each rental class? Super Saver Deluxe Business

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 Type II Super Saver $30 Rental Class $20 Deluxe $35 $30 Business $40 Type I rooms do not have high-speed Internet access and are not available for the Business rental class. 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, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. (a) Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Is the demand by any rental class not satisfied? Explain. If demand materializes as forecast, there will be rooms not reserved in the Super Saver class. (b) How many reservations can be accommodated in each rental class? Super Saver Deluxe Business

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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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 follows: Room Туре І Туре II Super Saver $30 Rental Class $20 Deluxe $35 $30 Business $40 Type I rooms do not have high-speed Internet access and are not available for the Business rental class. 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, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. (a) Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Is the demand by any rental class not satisfied? Explain. If demand materializes as forecast, there will be rooms not reserved in the Super Saver class. (b) How many reservations can be accommodated in each rental class? Super Saver Deluxe Business
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 Туре І Туре II Super Saver $30 Rental Class $20 Deluxe $35 $30 Business $40 Type I rooms do not have high-speed Internet access and are not available for the Business rental class. 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, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. (a) Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Is the demand by any rental class not satisfied? Explain. If demand materializes as forecast, there will be rooms not reserved in the Super Saver class. (b) How many reservations can be accommodated in each rental class? Super Saver Deluxe Business
(c) Management is considering offering a free breakfast to anyone upgrading from a Super Saver reservation to Deluxe class. If the cost of the breakfast to Round Tree is $5, should this incentive be offered? Increasing demand for Deluxe class accommodations will decrease profit. Since the predicted change in profit is less than breakfast, the incentive should be offered. the added cost of the (d) 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? Type I because this will increase profit by $ (e) 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? 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. 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. 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. 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.
Transcribed Image Text:(c) Management is considering offering a free breakfast to anyone upgrading from a Super Saver reservation to Deluxe class. If the cost of the breakfast to Round Tree is $5, should this incentive be offered? Increasing demand for Deluxe class accommodations will decrease profit. Since the predicted change in profit is less than breakfast, the incentive should be offered. the added cost of the (d) 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? Type I because this will increase profit by $ (e) 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? 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. 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. 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. 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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Decision Variables:

Suppose-xij be the no. of room type i allotted to different rental class represented by jWhere i = 1,2,3 and j= 1,2,3

 

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