To celebrate the recent addition of the Hospitality and Tourism Management (HTM) department in the Spears School of Business, here is a hypothetical wine blending problem.

All units are in barrels. You can blend 3 wines from 5 varietals of grapes, which have different characteristics of flavor and sugar (Brix). You know the maximum amount of each grape, and its assessed cost. You do not have to use all the grapes in production.

You want to blend 3 wines with the characteristics shown above. FLAVOR - is the limit of average flavor for each wine, BRIX is the lower and upper bound of the BRIX value, and Sales is the per barrel revenue associated with each of the three wine types that are blended.

Our goal in blending wines is to maximize sales less costs. Additional requirements besides the weighted averages of BRIX and FLAVOR - Wine 1 cannot have any one varietal make up more than 40% of the overall amount of Wine 1 produced. Each varietal must make up at least 15% of Wine 2's production. And any one varietal cannot make up more than 50% of Wine 3 produced.

You must make at least 50 barrels of each of the three wines. Additionally, an individual Wine cannot be more than 45% of the total wine produced. Finally - only integer decision variables.