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 Super Saver Deluxe Business Room Type I Type II $30 $35 $20 $30 $40 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 100 Type I rooms and 120 Type II rooms. (a) Formulate and solve a linear program to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. (Assume S₁ is the number of Super Saver rentals allocated to room type I, S₂ is the number of Super Saver rentals allocated to room type II, D₁ is the number of Deluxe rentals allocated to room type I, D₂ is the number of Deluxe rentals allocated to room type II, and B2 is the number of Business rentals allocated to room type II. Write your answers expressing the amount allocated in dollars.) Max s.t. Demand for Super Saver Demand for Deluxe Demand for Business Type I Rooms Type II Rooms
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 Super Saver Deluxe Business Room Type I Type II $30 $35 $20 $30 $40 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 100 Type I rooms and 120 Type II rooms. (a) Formulate and solve a linear program to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. (Assume S₁ is the number of Super Saver rentals allocated to room type I, S₂ is the number of Super Saver rentals allocated to room type II, D₁ is the number of Deluxe rentals allocated to room type I, D₂ is the number of Deluxe rentals allocated to room type II, and B2 is the number of Business rentals allocated to room type II. Write your answers expressing the amount allocated in dollars.) Max s.t. Demand for Super Saver Demand for Deluxe Demand for Business Type I Rooms Type II Rooms
Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter7: Economies Of Scale And Scope
Section: Chapter Questions
Problem 7.5IP
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Transcribed Image Text: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
Super Saver
Deluxe
Business
Room
Type I
Type II
$30
$35
$20
$30
$40
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 100 Type I rooms and 120 Type II rooms.
(a) Formulate and solve a linear program to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. (Assume S₁ is the number of Super Saver rentals allocated to room type I, S₂ is the number of
Super Saver rentals allocated to room type II, D₁ is the number of Deluxe rentals allocated to room type I, D₂ is the number of Deluxe rentals allocated to room type II, and B2 is the number of Business rentals allocated to room type II. Write your answers
expressing the amount allocated in dollars.)
Max
s.t.
Demand for Super Saver
Demand for Deluxe
Demand for Business
Type I Rooms
Type II Rooms
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