Problem $3-21($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

Type I rooms do not have high$-$speed Internet access and are not available for the Business rental class.

demand forecast for a particular night is $120$ rentals in the Super Saver class, $70$ rentals in the Deluxe class, and $55$ rentals in the Business class. Round Tree has $105$ Type I rooms and $120$ 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. If your answer is zero, enter $"0".$

Profit $=$$

Is the demand by any rental class not satisfied?

because

Super Saver rentals

will have to be turned away if demands materialize as forecast.

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