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 Room Type I Type II $30 $35 $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 140 rentals in the Super Saver class, 50 rentals in the Deluxe class, and 40 rentals 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. (Assume S is the number of Super Saver rentals allocated to room type I, S2 is the number of Super Saver rentals allocated to room type II, D is the number of Deluxe rentals allocated to room type I, D is the number of Deluxe rentals allocated to room type II, B is the number of Business rentals allocated to room type II. Write your answers expressing the amount allocated in dollars.) Max s.t. Demand for Super Saver Demand for Deluxe Demand for Business Type I Rooms Type II Rooms S1 S2 D1 D2 B 20 Report the number of reservations of each type management should accept for each rental class room type combination to maximize profit. Rental Class Super Saver Deluxe Business Type I Room Type II What is the profit (in dollars) obtained through this allocation of room reservations. $