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.

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.

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

b.How many reservations can be accommodated in each rental class?

Rental Class

# of reservations

SuperSaver

Deluxe

Business