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.

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.

to room type II$,B_2$ is the number of Business rentals allocated to room type II$.$ Write your answers expressing the amount allocated in dollars.$)$

$$

s$.$t$.$

Demand for Super Saver

Demand for Deluxe

Demand for Business

Type I Rooms

Type II Rooms

$s_1,s_2,D_1,D_2,B_{2}0$

Report the number of reservations of each type management should accept for each rental class room type combination to maximize profit,

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

Deluxe Business

Is the demand for any rental class not satisfied?

If demand materializes as forecast, there will be $$ rooms not reserved in the $---$ Select$--$ class.

$($c$)$ 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?

$-..,,$ because this will increase profit by