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 $30 $35 -
Type II $15 $25 $35
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 110 rentals in the Super Saver class, 55 rentals in the Deluxe class, and 40 rentals in the Business class. Round Tree has 90 Type I rooms and 110 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.
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) How many reservations can be accommodated in each rental class?
Rental Class No of Reservations
Super Saver I
Deluxe
Business
(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?
Type I Type II
Shadow Price $ $