The Potluck
The study tour group had four weeks to recover from their digestive issues and put together their videos for the class assignment, which were to be shared at a final meeting over a potluck supper. There were ten students in the class and each was tasked with preparing two dishes to share with the rest of the group — either an entrée, a side, or a dessert. In order to make this meal optimal, their tour guide, who doubled as their management science professor, decided to model it as an integer program.
He asked the students to rate themselves on their ability to prepare sweet or savory dishes and proteins or vegetables. Their ratings appear in the table. A reasonably balanced meal with plenty of choices calls for at least five entrées, at least six desserts, and at least six sides. The students agreed to bring two dishes apiece and breathlessly awaited the results of the optimization model.
| | Entrée | Side | Dessert |
| Aaron | 0.70 | 0.41 | 0.68 |
| Alex | 0.56 | 0.52 | 0.03 |
| Josh | 0.40 | 0.73 | 0.39 |
| Erin | 0.70 | 0.62 | 0.66 |
| Julie | 0.18 | 0.16 | 0.32 |
| Kassie | 0.88 | 0.37 | 0.11 |
| Lindy | 0.90 | 0.06 | 0.44 |
| MacGregor | 0.43 | 0.20 | 0.99 |
| Marlene | 0.86 | 0.81 | 0.02 |
| Tracy | 0.83 | 0.01 | 0.96 |
The constraint for the entrées is:
• AaE + AlE + JOE + EE + JuE + KE + LE + McE + MrE + TE ≥ 5.
• AaE + AlE + JOE + EE + JuE + KE + LE + McE + MrE + TE ≤ 5.
• AaE + AlE + JOE + EE + JuE + KE + LE + McE + MrE + TE > 5.
• AaE + AlE + JOE + EE + JuE + KE + LE + McE + MrE + TE < 5.
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