How do duality principles apply in linear programming?
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In linear programming, duality principles connect a primal problem to its dual, revealing that the optimal values of both are equal under strong duality and that the dual's objective value is always less than or equal to the primal's under weak duality. This relationship enhances problem-solving efficiency and understanding of resource allocation.
Duality principles in linear programming link a primal problem to its dual, where each primal constraint corresponds to a dual variable. The primal maximizes while the dual minimizes, providing insights into resource allocation and shadow prices. Solutions to both problems inform each other, allowing for a deeper understanding of the optimization landscape and enhancing decision-making.