Problem 8-21 (Algorithmic) 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 $38 $43 Type I Room Type II $16 $28 $45 Type I rooms do not have 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 140 rentals in the Super Saver class, 50 rentals in the Deluxe class, and 40 rentals in the Business class. Round Tree has 110 Type I rooms and 110 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. Variable # of reservations 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 Is the demand by any rental class not satisfied? Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. b. How many reservations can be accommodated in each rental class? # of Rental Class 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? 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? Why? The input in the box below will not be graded, but may be reviewed and considered by your instructor. d. If Cabinetmaker 2 has additional hours available, would the optimal solution change? Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. e. Suppose Cabinetmaker 2 reduced its cost to $38 per hour. What effect would this change have on the optimal solution? If required, round your answers for the proportions to three decimal places, and for the total cost to two decimal places. Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Oak 01 = 02 = O3 = Cherry C1 = C2 = C3 = Total Cost = $ Explain