Problem 1

You work for a company in Scotland that produces four varieties of scotch whiskey: red, black, blue, and gold. The production process of these whiskeys consists of blending six varieties of aged single malt mixtures (SMM). Each SMM contains a percentage of phenolic compounds and a percentage of aldehides that, when combined, give the whiskeys their corresponding aroma and flavor profile. Different combinations of the SMMs yield the different flavors required by each of the four whiskey varieties. Furthermore, given the aging process required to produce each SMM, their cost per liter of each SMM is also different (see Table 1).

In order to guarantee consistency in their aroma and flavor profile, depending on the variety, the whiskeys are required to have a minimum percentage of phenolic compounds and a maximum acceptable percentage of aldehides. These requirements, the selling prices and the minimum demand of each variety are given in Table 2.

You have 1,200 lt available of each SMM for the production process. Furthermore, the production plant cannot process more than 10,000 lt of whiskey in total.

1. Provide a formulation for this problem specifying the sets, parameters, decision variables, constraints, and objective function. You can provide a general or an explicit formulation.

2. Solve the problem using Gurobi.