Your solutions should $be$ clear and concise using appropriate mathematical

notation and equation formatting. Any equations should $be$ included $on$ separate

lines and NOT $be$ embedded within sentences. Written responses should also $be$

clear and concise and properly copy$-$edited for typos and grammatical errors prior

$to$ submission.

Round Tree Resort $is$ a hotel that provides two types $of$ rooms Mountain View

$(Room$ Type $I)$ and Street View $(Room$ Type $II),$ with three rental classes $as$ follows:

Super Saver, Deluxe, and Business Conference. The profit per night for each type

$of$ room and rental class $is$ listed $in$ Table A below. Note that all Business

Conference customers are assigned street view rooms $as$ these are located next $to$

the conference center $of$ the building.

Table $A$: Profit per Night $by$ Room Type and Rental Class

Round Tree's management makes a forecast $of$ the nightly demand $by$ rental class

for each night $in$ the future. $An$ optimization model should $be$ developed $to$

maximize profit and determine how many reservations $to$ accept for each rental

class. The average nightly demand forecast for rooms $in$ the Summer Vacation

Season $is130$ rooms $in$ the Super Saver class, $60in$ the Deluxe class, and $50in$ the

Business class. Round Tree will not make more reservations than the forecasted

amounts $of$ each reservation for each rental class. Round Tree has a $limited$ number

$of$ each type $of$ room. There are $100$ Mountain View Rooms and $120$ Street View

Rooms. The following decision variables should $be$ used $in$ the analysis, note that

there $isnoB1$ variable because all Business Conference attendants are assigned $a$

street view room:

Decision Variables

$S1=$ number $of$ Super Saver reservations taken for room type $I$

$S2=$ number $of$ Super Saver reservations taken for room type $II$

$D1=$ number $of$ Deluxe reservations taken for room type $I$

$D2=$ number $of$ Deluxe reservations taken for room type $II$

$B2=$ number $of$ Business reservations taken for room type $II$

Prepare solutions and written responses for the questions listed below.

List $of$ Questions $to$ Answer

Write out $an$ appropriate objective function for Round Tree's optimization

problem using the decision variables provided.

Write out the mathematical constraints that correspond $to$ the total number $of$

reservations that Round Tree will take for each $of$ the three rental classes each

night during the Summer Vacation Season.

Write out the mathematical constraints that correspond $to$ total number $of$

reservations Round Tree will take for each room type per night during the

Summer Vacation Season.

Assume that the optimization model was solved and indicated the following

proposed reservation policy should $be$ used $(listed$ below$).If$ this reservation

policy $is$ implemented, what happens $if$ Super Saver Demand ends $up$ being $130$

$as$ forecasted?

Proposed Solution

Under Consideration:

$S1=100$

$S2=10$

$D1=0$

$D2=60$

$B2=50$

Nightly Profit $=$$$7000Ifan$ existing space can $be$ converted $to$ create $20$ additional mountain street

view rooms $to$ increase $S2$ from $10to30,$ would this accommodate all the

forecasted demand for the Super Saver class? Please answer using either a simple

Yes $orNo$ for this question.

Next, for the space conversion considered $in$ question $5,$ calculate the

corresponding increase $in$ Nightly Profit associated with increasing $S2$ from $10to$

$30$ per night.