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 I   Deluxe   Business         Demand for - Select your answer -DeluxeSuper SaverBusinessItem 9 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 - Select your answer -Type IType IIItem 12 room.       Explain.   The input in the box below will not be graded, but may be reviewed and considered by your instructor.           (d) Could the linear programming model be modified to plan for the allocation of rental demand for the next night?   - Select your answer -YesNoItem 14       What information would be needed and how would the model change? Explain.   The input in the box below will not be graded, but may be reviewed and considered by your instructor.

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ISBN:9781337406659
Author:WINSTON, Wayne L.
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Chapter9: Decision Making Under Uncertainty
Section9.2: Elements Of Decision Analysis
Problem 2P
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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:

 

    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 I  
Deluxe  
Business  
   
  Demand for - Select your answer -DeluxeSuper SaverBusinessItem 9 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 - Select your answer -Type IType IIItem 12 room.
   
  Explain.
  The input in the box below will not be graded, but may be reviewed and considered by your instructor.
 
 
 
   
(d) Could the linear programming model be modified to plan for the allocation of rental demand for the next night?
  - Select your answer -YesNoItem 14
   
  What information would be needed and how would the model change? Explain.
  The input in the box below will not be graded, but may be reviewed and considered by your instructor.
 
 
 

 

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
Type I (Mountain View)
$35
$40
Room
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
06
Super Saver rentals allocated to room type II
15
Deluxe rentals allocated to room type I
Deluxe rentals allocated to room type II
55
Business rentals allocated to room type II
50
(b) For the solution in part (a), how many reservations can be accommodated in each rental class?
Rental Class
No of Reservations
Super Saver I
105
Deluxe
55
Business
50
Demand for Super Saver
V 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?
Турe I
Туре II
Shadow Price s
35
15
Convert an unused office area to Type I
room.
Explain.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
blank
(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.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
blank
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: Rental Class Super Saver Deluxe Business Type I (Mountain View) $35 $40 Room 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 06 Super Saver rentals allocated to room type II 15 Deluxe rentals allocated to room type I Deluxe rentals allocated to room type II 55 Business rentals allocated to room type II 50 (b) For the solution in part (a), how many reservations can be accommodated in each rental class? Rental Class No of Reservations Super Saver I 105 Deluxe 55 Business 50 Demand for Super Saver V 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? Турe I Туре II Shadow Price s 35 15 Convert an unused office area to Type I room. Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank (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. The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank
Expert Solution
Step 1: Linear programming Problem

S1 = Super Saver Type 1 rooms

S2 = Super saver Type 2 rooms

D1 = Deluxe Type 1 rooms

D2 = Deluxe Type 2 rooms

B2 = Busienss Type 2 rooms.

The Excel model would be as follows.

Operations Management homework question answer, step 1, image 1

The formulas used are as follows.

Operations Management homework question answer, step 1, image 2

 

 

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ISBN:
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Author:
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Publisher:
Cengage,