Question

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	$36	$38	—
	Type II	$15	$26	$38

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, 60 rentals in the Deluxe class, and 40 rentals in the Business class. Round Tree has 125 Type I rooms and 135 Type II rooms.

1. 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

   
   Is the demand by any rental class not satisfied?

Answer 1

The decision variable in Green
The constrains are in Blue
And the objective function is in Orange

			Rental Class
			Super Saver	Deluxe	Business
		Type I	36	38	-
	Room	Type II	15	26	38	Constrain 4,5,
Variable for decision	No of rooms	Type 1	125	0	0	125	<=	125	Type 1 room restriction
No of rooms	Type 2	15	60	40	115	<=	135	Type 2 room restriction
Contrain 1,2,3	Sum of rooms	140	60	40
		<=	<=	<=
	Demand	140	60	40
room restriction
Optimization of profit			7805

A.

Variable	# of reservations
SuperSaver rentals allocated to room type I	125
SuperSaver rentals allocated to room type II	15
Deluxe rentals allocated to room type I	0
Deluxe rentals allocated to room type II	60
Business rentals allocated to room type II	40

B

Rental Class	# of reservations
SuperSaver	140
Deluxe	60
Business	40

C.

Yes

Profit for Type 1 is Deluxe over Super Saver is $2

Profit for Type 2 is Deluxe over Super Saver is $9

On average the cost is $5.5, so it is still profitable if $5 breakfast is given.

D.

Type 1.

As the average profit is $37 for type 1, which is much higher than Type 2.

E.

Yes,

With vacancy of the rooms and demand for the next.