The Robinsons are planning a wedding and reception for their daughter, Rachel. Some of the most expensive items served at the reception and dinner are wine and beer. The Robinsons are planning on 200 guests at the reception, and they estimate that they need at least four servings (i.e., a glass of wine or bottle of beer) for each guest in order to be sure they won’t run out. A bottle of wine contains five glasses. They also estimate that 50% more guests will prefer wine to beer. A bottle of wine costs $8, and a bottle of beer costs $0.75. The Robinsons have budgeted $1,200 for wine and beer. Finally, the Robinsons want to minimize their waste (i.e., unused wine and beer). The caterer has advised them that typically 5% of the wine and 10% of the beer will be left over. How many bottles of wine and beer should the Robinsons order?
a. Formulate a linear programming model for this problem.
b. Solve this model graphically.