O 14, 15) 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 Type 1 (Mountain View) Room Type 1 (Street View) Super Saver Deluxe Business $35 $40 $25 $35 545 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 cars. The demand forecast for a particular night 150 rentals in the Super Saver class, 55 in the Deluxe class, and 40 in the Business cons Since these are the forecasted demands, Round Tree will take no more than these amounts of each reservation for each rental class Hound Tree has a limited number of each type of room. There are 100 Type 1 rooms and 110 Type 1 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 entero Rental Class with room type No. of Reservations Super Saver rentals allocated to room type 1 95 Super Saver rent located to room type 11 0 Deluxerentes allocated to room type 1 5 Deluxe rentals allocated to room type II 60 Business rentals allocated to room type It 50 (b) For the solution in part (o), how many reservations can be accommodated in each rental caus? Rental Class No. of Reservations Super Saver 95 Deluxe 65 Business 50 Demand for Super Saver rental class was not satisfied Business SO Demand for Super Saver 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 lor a Type 11 room? Type 1 Type 1 Shadow Prices 35 30 Convert an unused office area to Type 1 room Explain Converting the unused mice area to this type of room Increases profit by : 35 (d) Could the linear programming model be modified to plan for the allocation of rental demand for the next night? Yes What information would be needed and how would the model change? Explain (1) We would need a forecast of demand for each rental dass on the next night to use as the right hand sides of the first three constraints (H) We would need to know if Type 1 rooms can be used as business classrooms the next night and add a variable to the objective function (18) We would need to know how many rooms of Type I and Type I there will be on the next night to use as the right hand sides of the last two constraints (iv) 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 Option (0) O 14, 15) 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 Type 1 (Mountain View) Room Type 1 (Street View) Super Saver Deluxe Business $35 $40 $25 $35 545 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 cars. The demand forecast for a particular night 150 rentals in the Super Saver class, 55 in the Deluxe class, and 40 in the Business cons Since these are the forecasted demands, Round Tree will take no more than these amounts of each reservation for each rental class Hound Tree has a limited number of each type of room. There are 100 Type 1 rooms and 110 Type 1 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 entero Rental Class with room type No. of Reservations Super Saver rentals allocated to room type 1 95 Super Saver rent located to room type 11 0 Deluxerentes allocated to room type 1 5 Deluxe rentals allocated to room type II 60 Business rentals allocated to room type It 50 (b) For the solution in part (o), how many reservations can be accommodated in each rental caus? Rental Class No. of Reservations Super Saver 95 Deluxe 65 Business 50 Demand for Super Saver rental class was not satisfied Business SO Demand for Super Saver 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 lor a Type 11 room? Type 1 Type 1 Shadow Prices 35 30 Convert an unused office area to Type 1 room Explain Converting the unused mice area to this type of room Increases profit by : 35 (d) Could the linear programming model be modified to plan for the allocation of rental demand for the next night? Yes What information would be needed and how would the model change? Explain (1) We would need a forecast of demand for each rental dass on the next night to use as the right hand sides of the first three constraints (H) We would need to know if Type 1 rooms can be used as business classrooms the next night and add a variable to the objective function (18) We would need to know how many rooms of Type I and Type I there will be on the next night to use as the right hand sides of the last two constraints (iv) 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 Option (0)
