Chapter 8, Problem 5P

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 high-speed 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 130 rentals in the Super Saver class, 60 in the Deluxe class, and 50 in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms.

1. 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.
2. b. For the solution in part (a), how many reservations can be accommodated in each rental class? Is the demand for any rental class not satisfied?
3. 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?
4. 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?