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:

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 $120$

rentals in the Super Saver class, $65$ rentals in the Deluxe class, and $40$ rentals in the Business class. Round Tree has $105$ Type I rooms and $115$

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.

Is the demand by any rental class not satisfied?