1. 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 (Mountain View)

$30

$35

Type II (Street View)

$20

$30

$40

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. Since these are the forecasted demands, Round Tree will take no more than these amounts of each reservation for each rental class. Round Tree has a limited number of each type of room. There are 100 Type I rooms and

120 Type II rooms.

1. 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. 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. 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 convert- ing the office to a Type I or a Type II room? Why?
4. 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?