Linear programming duality is a mathematical concept that states that for every linear programming problem, there exists a dual problem that is closely related to it.
Linear programming duality works by taking a linear programming problem and creating a related problem known as the dual problem. The dual problem has the same number of variables as the original problem but has a different objective function and constraints.
The primal and dual problems in linear programming duality are closely related and are said to be dual to each other. This means that the solution to one problem can be used to find the solution to the other problem, and the optimal values of the objective functions in both problems will be equal.
Linear programming duality is useful because it allows for a deeper understanding of a linear programming problem by providing a different perspective. It also allows for the creation of efficient algorithms for solving linear programming problems.
Linear programming duality has various applications in fields such as economics, operations research, and engineering. It can be used to solve optimization problems, find optimal solutions to resource allocation problems, and analyze the efficiency of different systems.