Round Tree Manor is a hotel that provides two types of rooms with three rental c
ID: 470433 • Letter: R
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:
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.
Rental ClassRoom Super Saver Deluxe Business Type I $38 $43 — Type II $16 $28 $45
Explanation / Answer
Let us define the LPP model in the standard structure,
Objective Function: Total profit from reservations
Decision Variables: No. of reservations for each type of room and in each class.
Constraints:
Capacity constraints: No. of reservations cannot be more than total capacity per type, that is 110.
Demand constraints: No. of reservations cannot be more than the demand different for each class.
No. of reservations should be an integer.
The formulated model in the Excel is given below; solve the LPP problem using solver to maximize profit with given constraints, the solution is given below;
a. No. of reservations to be accepted
From the solver solution as given below;
The Super saver class can not satisfy the demand of 140 reservations including both type 1 and type 2 rooms. Though all the type 1 room allocated for Supersaver class, only 30 type 2 rooms are allocated for super saver class. The reason for this is clear that the profit from type 1 room is more than that of type 1 room.
b. No. of Reservations per class
Rental Class
c. Free breakfast for Deluxe room upgradation
Free breakfast for upgrading Super Saver to Deluxe class rooms will reduce the profit of Deluxe class rooms by $5 each;
Hence, reforming the model with revised profits for Deluxe class and slving using solver;
The total profit is $7450 which is less than the original profit of $7700. So offering the breakfast incentive does not increase the profit and hence it should not be offered.
d. Conversion of office space into rental room;
The office space shall be converted into a type 1 room. The reason, the demand for Super Saver class is not satisfied and the profit for type 1 room for this particular class is more than type 2 room.
Hence, converting office space into type 1 room will satisfy the demand for Super saver class and will maximize the overall profits.
e. No, there will be modification in the LPP model in the allocation of the rooms since the allocation is done for every night based upon the profit per night.
# of reservations SuperSaver rentals allocated to room type I 110 SuperSaver rentals allocated to room type II 20 Deluxe rentals allocated to room type I 0 Deluxe rentals allocated to room type II 50 Business rentals allocated to room type II 40Related Questions
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