What is the purpose of a feasibility table in optimization?

The purpose of a feasibility table in optimization, particularly in the context of linear programming and decision-making, is to show feasible combinations of binary variables. This table serves as a visual aid that allows decision-makers to assess which combinations of binary variables meet the defined constraints of the problem.

In optimization problems where variables can only take on binary values (0 or 1), a feasibility table outlines the possible configurations that satisfy all constraints, thus helping in identifying valid solutions to the optimization problem. By listing these combinations, the feasibility table becomes a critical tool for determining which options are viable before proceeding to the next steps in the optimization process, such as finding the objective function's value or maximizing profit.

In contrast, other options do not accurately reflect the primary use of a feasibility table. For instance, simply listing all possible constraints does not provide the combination structures needed for analysis, nor does calculating maximum profit or providing definitive answers to all variables align with the specific function of a feasibility table. Thus, highlighting the feasible combinations of binary variables is the essential aspect that underscores the role of the feasibility table in the optimization context.