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 Busines Room Type I $25 $30 Type II $20 $30 $40 Type I rooms do not have high speed 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 120 rentals in the Super Saver class, 55 in the Deluxe class, and 50 in the Business class Round Tree has 90 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 Rental Class with room type No of Reservations Super Saver rentals allocated to room type I Super Saver 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 (b) For the solution in part (a), how many reservations can be accommodated in each rental class Rental Class No of Reservations Super Saver I Deluxe Business Demand for rental class was not satisfied (c) 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 Type I Type II Shadow Price $ $ Convert an unused office area to room Explain The input in the box below will not be graded, but may be reviewed and considered by your instructor blank (d) 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 Explain

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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

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 Busines

Room Type I $25 $30

Type II $20 $30 $40

Type I rooms do not have high-speed 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 120 rentals in the Super Saver class, 55 in the Deluxe class, and 50 in the Business class. Round Tree has 90 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.

Rental Class with room type	No of Reservations
Super Saver rentals allocated to room type I
Super Saver 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

(b)

For the solution in part (a), how many reservations can be accommodated in each rental class?

Rental Class	No of Reservations
Super Saver I
Deluxe
Business

Demand for

rental class was not satisfied.

(c)

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?

	Type I	Type II
Shadow Price	$	$

Convert an unused office area to

room.

Explain.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

blank

(d)

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? Explain.

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