Duality

Associated with any LPP is another LPP, called its dual. The first way of stating Linear Problem is called the Primal of the problem. The scion what of staling the same problem is called  the dual. In other words each LP maximizing problem has its corresponding dual, a Munising problem. Similarly each LP maximizing problem ahs its corresponding dual, a minimizing problem. Similarly each LP Minising problem has its corresponding dual a maximizing problem. It is an interesting feature of the simplex method, tat we can use it to solve, it will also give the solution to the other problem.

The optimal solution for the primal and the dual are equivalent but they are derived through alternative procedures. The dual contains economic information useful to management and it maximizing a profit function subject less than or equal to resource constraints, the dual will involve minimizing total opportunity cost subject to greater than or equal to product profit constraints. Formulating the dual problem from a given primal is not difficult, and once it is formulated, the solution procedure is exactly same as for any LP problem.

It may be noted that, some times it is computationally easier to solve the dual than the primal. The primal problem could take seven or more simplex tables to reach an optimum solution.

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