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 high-speed 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.
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”.
Variable # of reservations
SuperSaver rentals allocated to room type I fill in the blank 1
SuperSaver rentals allocated to room type II fill in the blank 2
Deluxe rentals allocated to room type I fill in the blank 3
Deluxe rentals allocated to room type II fill in the blank 4
Business rentals allocated to room type II fill in the blank 5
Profit = $ fill in the blank 6
Is the demand by any rental class not satisfied?
because fill in the blank 8
will have to be turned away if demands materialize as forecast.
How many reservations can be accommodated in each rental class?
Rental Class # of reservations
SuperSaver fill in the blank 10
Deluxe fill in the blank 11
Business fill in the blank 12
Management is considering offering a free breakfast to anyone upgrading from a Super Saver reservation to Deluxe class. If the cost of the breakfast to Round Tree is $5, should this incentive be offered?
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 converting the office to a Type I or a Type II room?
Why?
A Type I room has a shadow price of $ fill in the blank 15
which means that if you add one more Type I room you will increase your profit by $ fill in the blank 16
. A Type II room has a shadow price of $ fill in the blank 17
which means that if you add one more Type II room you will increase your profit by $ fill in the blank 18
. Since more profit is desirable, you would convert it to a
room.
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?
We would need the
for each rental class on the next night. Using the forecast, we would modify the
sides of the first three constraints and resolve.
