What is the dual problem in linear programming, and how does it relate to shadow prices?
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The dual problem is derived from the primal linear programming problem and provides insights into the values of resources. The optimal solution to the dual problem gives the shadow prices for the constraints in the primal problem, linking both problems in a meaningful way.
The dual problem in linear programming represents the constraints of the original (primal) problem as variables and the objective as constraints, with its solution providing shadow prices, which indicate the marginal value of relaxing a constraint.
The dual problem in linear programming is a mathematical formulation derived from the original problem, known as the primal problem. Each primal LP problem can be associated with a dual problem that provides a different perspective on the same optimization scenario.