Problem 8-21 (Algorithmic) 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 ren

1. Problem 8-21 (Algorithmic)

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:

Type I rooms do not have wireless 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 120 rentals in the Super Saver class, 70 rentals in the Deluxe class, and 55 rentals in the Business class. Round Tree has 105 Type I rooms and 120 Type II rooms.

1. 1. Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types.

      Variable	# of reservations
      SuperSaver rentals allocated to room type I	fill in the blank 1
      SuperSaver rentals allocated to room type II	fill in the blank 2
      Deluxe rentals allocated to room type I	fill in the blank 3
      Deluxe rentals allocated to room type II	fill in the blank 4
      Business rentals allocated to room type II	fill in the blank 5

   2. 
      Is the demand by any rental class not satisfied?
       
      Explain.
      The input in the box below will not be graded, but may be reviewed and considered by your instructor.
      

   3. How many reservations can be accommodated in each rental class?

      Rental Class	# of reservations
      SuperSaver	fill in the blank 8
      Deluxe	fill in the blank 9
      Business	fill in the blank 10

   5. 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?
       

   6. 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?
      The input in the box below will not be graded, but may be reviewed and considered by your instructor.
      

   7. 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?
      The input in the box below will not be graded, but may be reviewed and considered by your instructor.