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: $($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?

Convert an unused office area to

oom.

Explain.

Converting the unused office area to this type of room increases profit by

$($d$)$ 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? Explain.

$($i$)$ We would need a forecast of demand for each rental class on the next night to use as the right$-$hand sides of the first three constraints

$($ii$)$ We would need to know if Type $1$ rooms can be used as Business class rooms the next night and add a variable to the objective function.

$($iii$)$ We would need to know how many rooms of Type I and Type II there will be on the next night to use as the right$-$hand sides of the last two constraints.

$($iv$)$ We would need to know whether the profit per night of each type of room and rental class will change and use these as objective coefficients.

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. If an amount is zero, enter $"0".$

$($b$)$ For the solution in part $($a$),$ how many reservations can be accommodated in each rental class?

Demand for $-$ Select your answer $-$ rental class was not satisfied.