What is duality in linear programming, and how is the dual problem related to the primal problem?
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Duality in linear programming refers to the relationship between a primal problem and its corresponding dual problem. Each primal maximization problem has a dual minimization problem. The optimal solution of the primal provides bounds on the optimal solution of the dual, and vice versa. If one problem is feasible and bounded, so is the other, and their optimal values are equal.
Duality in linear programming connects a primal problem and its dual, where each reflects the other's solution. The primal seeks to optimize an objective function under constraints, while the dual reverses the roles of coefficients and constraints. The strong duality theorem states that if one has an optimal solution, so does the other, with equal objective values, enhancing understanding and efficiency in solving LP problems.