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. Room types include supersaver rentals type $1,$ Supersaver rentals type II$,$ Delux rentals type $1,$ delux rentals type II$,$ and business rentals type II$.$

b$.$ How many reservations can be accommodated in each rental class?

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.

e$.$ Could the linear programming model be modified to plan for the allocation of rental demand for the next night?

What information would be needed and how would the model change?

The input in the box below will not be graded, but may be reviewed and considered by your instructor.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:

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 $120$

rentals in the Super Saver class, $65$ rentals in the Deluxe class, and $40$ rentals in the Business class. Round Tree has $105$ Type I rooms and $115$

Type II rooms.