Question

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:
Rental Class


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

Answer 1

To determine how many reservations to accept in each rental class and how to allocate the reservations to room types, linear programming can be used. The goal is to maximize profit. Constraint equations and an objective function are used to find the optimal solution.

Step-by-step explanation:

To determine how many reservations to accept in each rental class and how to allocate the reservations to room types, we can use linear programming. The goal is to maximize profit. 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.

Let's set up decision variables for the number of reservations to accept in each rental class. Let's call these variables S (for Super Saver), D (for Deluxe), and B (for Business). We also have constraint equations:

1. The total number of Super Saver reservations should be less than or equal to 140: S <= 140.
2. The total number of Deluxe reservations should be less than or equal to 50: D <= 50.
3. The total number of Business reservations should be less than or equal to 40: B <= 40.
4. Since Type I rooms do not have wireless Internet access and are not available for the Business class, the number of Business reservations should be 0: B = 0.

Additionally, we have the following constraint equations for the number of reservations in each room type:

1. The total number of Type I room reservations should be less than or equal to 110: S + D <= 110.
2. The total number of Type II room reservations should be less than or equal to 110: S + D + B <= 110.

Finally, we have the objective function to maximize profit:

Profit = 38S + 43D + 16S + 28D + 45B

We can now use linear programming techniques to solve this problem and find the optimal number of reservations to accept in each rental class and how to allocate the reservations to room types.

Answer 2

Step-by-step explanation:

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:

Rental Class