Abstract
The chapter provides an overview on the concept of duality in linear programming. The concept of duality plays an important role in linear programming from the theoretical as well as a practical point of view. Another associated linear programming problem is called as dual problem. The original problem is called the primal problem. The relations between these two problems are such that it is possible to use the optimal basic feasible solution of one problem to obtain an optimal solution for the other readily. A number of theorems including weak duality theorem, duality theorem, unboundedness theorem, and existence theorem are presented in the chapter to show the relations between the primal and the dual problems. The chapter also describes how duality relations in linear programming can be used in proving some important results along with the consideration of economic interpretation of a pair of dual problems in linear programming. The basic ingredients of all economic problems are inputs, outputs, and profit.
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