# Duality in Linear Programming

## Quantitative Methods: Duality in Linear Programming

Associated with every linear programming problem, there is another intimately related LPP, called the dual problem of the original LPP. The original LPP is called the Primal Problem. According to the duality theorem:
“For every maximization (or minimization) problem in linear programming, there is a unique similar problem of minimization (or maximization) involving the same data which describes the original problem.”

The rules for constructing the Dual from the Primal (or Primal from the Dual) are:
i) If the objective of one problem is to be maximized, the objective of the other is to be minimized.
ii) The maximization problem should have all ≤ constraints and the minimization problem has all ≥ constraints.
iii) All primal and dual variables must be non-negative (> 0).
iv) The element of the right hand side of the constraints in one problem are the respective coefficient of the objective functions in the other problem.
v) The matrix of constraints coefficients for one problem is the transpose of the matrix of constraint coefficients for the either problem.

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