In: Math
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  | 
 $38  | 
 $43  | 
 —  | 
|
| 
 Type II  | 
 $16  | 
 $28  | 
 $45  | 
|
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 140 rentals in the Super Saver class, 50 rentals in the Deluxe class, and 40 rentals in the Business class. Round Tree has 110 Type I rooms and 110 Type II rooms.
| 
 Variable  | 
 # of reservations  | 
| 
 SuperSaver rentals allocated to room type I  | 
|
| 
 SuperSaver 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  | 
| 
 Rental Class  | 
 # of reservations  | 
| 
 SuperSaver  | 
|
| 
 Deluxe  | 
|
| 
 Business  | 
| 
 Variable  | 
 # of reservations  | 
| 
 SuperSaver rentals allocated to room type I  | 
110 | 
| 
 SuperSaver rentals allocated to room type II  | 
20 | 
| 
 Deluxe rentals allocated to room type I  | 
0 | 
| 
 Deluxe rentals allocated to room type II  | 
50 | 
Business rentals allocated to room type II 40
| 
 Rental Class  | 
 # of reservations  | 
| 
 SuperSaver  | 
130 | 
| 
 Deluxe  | 
50 | 
Business 40

