The idea of duality in linear programming states that each primal problem (a linear programming problem) has a corresponding dual problem that presents a different angle on the same optimization situation. The dual problem reformulates these elements by reversing the roles of the objective function and the constraints, whereas the primal problem aims to maximize or minimize an objective function under specific constraints. Because of this relationship, more effective solutions and a deeper comprehension of the dynamics of resource allocation are made possible by the optimal solution to the dual problem offering insights into the primal problem, such as shadow pricing or the marginal value of resources.

Duality in linear programming refers to the concept that every linear program (the primal) has a corresponding dual program

based upon same data and having the same solution.