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 Type I $36 $38 Room Type II $15 $26 $38 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, 60 rentals in the Deluxe class, and 40 rentals in the Business class. Round Tree has 125 Type I rooms and 135 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?