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Problem 3-21 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 Type I $30 $35 Room Type II $20 $30 $40 Type I rooms do not have high-speed Internet access and areot 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 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. Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Enter "O" if your answer is zero. Variable SuperSaver rentals allocated to room type I SuperSaver 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 # of reservations 100 Profit- Is the demand by any rental class not satisfied? Explain. X Super Saver rentals will have to be turned away if demands materialize as forecast. b. How many reservations can be accommodated in each rental class? Rental Class! # of reservations SuperSaver Deluxe Business c. Management is considering offering a free breakfast to anyone upgrading from a Super Saver reservation to Deluxe class. If the cost of the breakfast to Round Tree is $5, should this incentive be offered? Yes d. 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 1 Why? A Type I room has a shadow price of $ which means that if you add one more Type I room you will increase your profit by$ .A Type II room has a shadow price of which means that if you add one more Type II room you will increase your profit by $ Since more profit is desirable, you would convert it to a Type I room e. Could the linear programming model be modified to plan for the allocation of rental demand for the next night