Formulate a Mixed-Integer Linear Programming (MILP) problem to determine which company a household should choose for at least 3000 minutes of long-distance telephone calls monthly.

To solve a household's decision on which phone company to use for long-distance telephone calls, we can use a MILP problem formulation with constraints and an objective to maximize the total minutes used.

Explanation:

To solve a household's decision on which phone company to use for long-distance telephone calls, we can use a MILP (Mixed-Integer Linear Programming) problem formulation. We need to define decision variables and constraints to optimize the choice. Let's assume there are three companies to choose from: A, B, and C. Let xA, xB, and xC represent the number of minutes used with each company, respectively.

The objective function can be formulated as: maximize Z = xA + xB + xC, subject to the constraint xA + xB + xC ≥ 3000. This ensures that the total minutes used by all three companies is at least 3000. Additionally, we can add constraints to limit the usage for each company, such as xA ≤ 2000, xB ≤ 2500, and xC ≤ 1500, to represent company-specific limits.