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

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Type I (Mountain View) $30 $35 -

Room

Type II (Street View) $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 130 rentals in the Super Saver class, 60 in the Deluxe class, and 50 in the Business class. Since these are the forecasted demands, Round Tree will take no more than these amounts of each reservation for each rental class. Round Tree has a limited number of each type of room. There are 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. If an amount is zero, enter "0".

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 -Select your answer- Deluxe OR Super Saver OR Business _______ rental class was not satisfied.

(c) With a little work, an unused office area could be converted to a re

ntal 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 : Type I OR Type II ____________room.

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

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(d) Could the linear programming model be modified to plan for the allocation of rental demand for the next night? Yes OR No _________

What information would be needed and how would the model change? Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor.

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