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 (Mountain View) $30 $35 Room Type II (Street View) $20 $40 Round Tree's management makes a forecast of the demand by rental class for each night 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 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 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 Super Saver rentals allocated to room type I Super Saver rentals allocated to room type II No. of Reservations 100 10 Deluxe rentals allocated to room type I Deluxe rentals allocated to room type II 0 60 Business rentals allocated to room type II 50 (b) For the solution in part (a), how many reservations can be accommodated in each rental class? Rental Class Super Saver Deluxe Business No. of Reservations 110 60 Y 50 Demand for Super Saver 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 $ 30 Convert an unused office area to Type I 20 Vroom. Explain. Converting the unused office area to this type of room increases profit by $ (d) Could the linear programming model Yes 20 x 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. (1) We would need to know how many rooms of Type I and Type II there will be on the next night to use as the right-hand sides of the last two constraints. (II) We would need to know whether the profit per night of each type of room and rental class will change and use these as objective coefficients. (III) We would need to know if Type 1 rooms can be used as Business class rooms the next night and add a variable to the objective function. (iv) We would need a forecast of demand for each rental class on the next night to use as the right-hand sides of the first three constraints Option (Iv)