Hanson Inn is a 96-room hotel located near the airport andconvention center in Louisville, Kentucky. When a convention or aspecial event is in town, Hanson increases its normal room ratesand takes reservations based on a revenue management system. TheClassic Corvette Owners Association scheduled its annual conventionin Louisville for the first weekend in June. Hanson Inn agreed tomake at least 50% of its rooms available for convention attendeesat a special convention rate in order to be listed as a recommendedhotel for the convention. Although the majority of attendees at theannual meeting typically request a Friday and Saturday two-nightpackage, some attendees may select a Friday night only or aSaturday night only reservation. Customers not attending theconvention may also request a Friday and Saturday two-nightpackage, or make a Friday night only or Saturday night onlyreservation. Thus, six types of reservations are possible:convention customers/two-night package; convention customers/Fridaynight only; convention customers/Saturday night only; regularcustomers/two-night package; regular customers/Friday night only;and regular customers/Saturday night only.
The cost for each type of reservation is shown here:
| Two-Night
Package | Friday Night
Only | Saturday Night
Only |
| Convention | $225 | $123 | $130 |
| Regular | $295 | $146 | $152 |
The anticipated demand for each type of reservation is asfollows:
| Two-Night
Package | Friday Night
Only | Saturday Night
Only |
| Convention | 40 | 20 | 15 |
| Regular | 20 | 30 | 25 |
Hanson Inn would like to determine how many rooms to makeavailable for each type of reservation in order to maximize totalrevenue.
- Define the decision variables and state the objective function.Round your answers to the nearest whole number.
| Let | CT = number of convention two-night rooms |
| CF = number of convention Friday only rooms |
| CS = number of convention Saturday only rooms |
| RT = number of regular two-night rooms |
| RF = number of regular Friday only rooms |
| RS = number of regular Saturday only room |
- Formulate a linear programming model for this revenuemanagement application. Round your answers to the nearest wholenumber. If the constant is \"1\" it must be entered in the box.
| 1) | CT | | | | | | | | |
| 2) | CF | | | | | | | | |
| 3) | CS | | | | | | | | |
| 4) | RT | | | | | | | | |
| 5) | RF | | | | | | | | |
| 6) | RS | | | | | | | | |
| 7) | CT | + | CF | | | | | | |
| 8) | CT | + | CS | | | | | | |
| 9) | CT | + | CF | + | RT | + | RF | | |
| 10) | CT | + | CS | + | RT | + | RS | | |
| 11) | CT, | CF, | CS, | RT, | RF, | RS | | | 0 |
- What are the optimal allocation and the anticipated totalrevenue? Round your answers to the nearest whole number.
| Variable | Value |
| CT | |
| CF | |
| CS | |
| RT | |
| RF | |
| RS | |
Total Revenue = $Â Â
- Suppose that one week before the convention the number ofregular customers/Saturday night only rooms that were madeavailable sell out. If another nonconvention customer calls andrequests a Saturday night only room, what is the value of acceptingthis additional reservation? Round your answer to the nearestdollar.
The dual value for constraint 10 shows an added profit of$Â Â Â if this additional reservation is accepted.
