Dual linear-programming problem

A companion problem defined by a linear-programming problem. Every linear-programming problem has an associated dual-programming program. When the linear-programming problem has the form

then its dual problem is also a linear-programming problem with the form

The original problem is called the primal problem. If the primal minimization problem is given as equations in nonnegative variables, then its dual is a maximization problem with less than or equal to constraints whose variables are unrestricted (free). The optimal solutions to primal and dual problems are strongly interrelated. Complementary slackness theorem; Duality theorem ; Symmetric dual problem; Unsymmetric dual problem.