Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super…

Round Tree Manor Problem
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.
Profit per night (dollars)
Rental Class
Super Saver
Deluxe
Business
Room Type I
$30
$35
—
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 profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 150 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 S1 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, D1 is the number of Deluxe rentals allocated to room type I, D2 is the number of Deluxe rentals allocated to room type II, B2 is the number of Business rentals allocated to room type II. Write your answers expressing the amount allocated in dollars.)
Report the number of reservations of each type management should accept for each rental class room type combination to maximize profit.
Allocation of reservations
Rental Class
Super Saver
Deluxe
Business
Room Type I
—
Type II
What is the profit (in dollars) obtained through this allocation of room reservations. $
(b)
For the solution in part (a), how many reservations can be accommodated in each rental class?
Super Saver
Deluxe
Business
Is the demand for any rental class not satisfied? If demand materializes as forecast, there will be rooms not reserved in the – Super Saver Deluxe Business class.
Help with part A and B