duality

The dual problem is an LP defined directly and systematically from the primal (or original) LP model. The two problems are so closely related that the optimal solution of one problem automatically provides the optimal solution to the other.
The dual is defined for various forms of the primal depending on the sense of optimization (maximization or minimization), types of constraints (?, ?, or =), and orientation of the variables (nonnegative or unrestricted).The primal and dual solutions are so closely related that the optimal solution of either problem directly yields (with little additional computation) the optimal solution to the other.Thus, in an LP model in which the number of variables is considerably smaller than the number of constraints, computational savings may be realized by solving the
dual, from which the primal solution is determined automatically there are two methods for determining the dual values. Note that the dual of the dual is itself the primal, which means that the dual solution can also be used to yield the optimal primal solution automatically.