Linear Programming

Please formulate the constraints for this problem as well as solutions to parts c and d.

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Round Tree Manor is a hotel that has two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit contribution per night for each type of room and rental class is as follows:

(see attached file for chart)

Type I rooms do not have 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 could be used to determine the number of reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms.

a. Formulate a linear programming model that can be used to determine the number of reservations to accept in each rental class and how these reservations should be allocated to room types.

b. Determine the number of reservations that can be accommodated in each rental class and whether the demand by any rental class is not satisfied.

c. Management is considering offering a free breakfast to anyone upgrading from a Super Saver reservation to Deluxe class. If the cost to Round Tree Manor of providing the breakfast is $5, determine if this incentive should be offered.

d. With a little work, an unused office area could be converted to a rental room. Assuming that the conversion cost is the same for both types of rooms, provide a recommendation and explanation for converting the office to a Type I or a Type II room.
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