Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver. Deluxe, and Business. The prot per night for each type of room and rental class is as follows. Rental Class super saver Deluxe Business Type I 3530 $35 Room Type II $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 prot is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 160 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 1 rooms and 120 Type 11 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 5]. is the number of Super Saver rentals allocated to room type I, 52 is the number of Super Saver rentals allocated to room type 11, D1 is the number of Deluxe rentals allocated to room type 1, 02 is the number of Deluxe rentals allocated to room type [1, .B2 is the number of Business rentals allocated to room type II. Write your answers expressing the amount allocated in dollars.) 4032 + 3501 + 30132 + 3031 + 2032 Max V s.t. Demand for Super Saver S1 + 52 S 160 V Demand for Deluxe D1 + D2 S 50 J Demand for Business 32 S 4'3 J Type I Roamg D1 + S1 S 100 V Type II Rooms 32 + D2 + S2 S 120 31' 32, 01' Dz, 52 Z D Report the number of reservations of each type management should accept for each rental class room type combination to maximize profit. I I Rental Class Demand for Deluxe D, + D, 5 50 Demand for Business B, 5 40 Type I Rooms Dits, 100 Type II Rooms By + D, + S, S 120 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 100 X Room Type II X X 40 What is the profit (in dollars) obtained through this allocation of room reservations. $ X (b) For the solution in part (a), how many reservations can be accommodated in each rental class? Super Saver Deluxe X Business Is the demand for any rental class not satisfied? If demand materializes as forecast, there will be X rooms not reserved in the Super Saver v class