A computational tool exists that derives the dual form of a linear program. This instrument accepts as input a linear programming problem, expressed in either standard or canonical form, and algorithmically generates its corresponding dual problem. The result specifies a new optimization problem that is mathematically related to the original, primal problem. As an instance, given a minimization problem with inequality constraints, the instrument produces a maximization problem with corresponding constraints derived from the primal.
The utility of such a device lies in its ability to simplify complex optimization challenges, provide economic interpretations of solutions, and offer computational advantages. Historically, the concept of duality in linear programming has been instrumental in algorithm development and sensitivity analysis. The generated dual offers insights into the shadow prices associated with the primal constraints, revealing the marginal value of resources. Moreover, under certain conditions, solving the dual problem can be computationally more efficient than solving the original problem, particularly when the primal has a large number of constraints.