Whenever a constraint has negative slack,the shadow price is zero.

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Negative slack in a constraint indicates that the constraint is binding, and the shadow price (or dual value) for a binding constraint is typically not zero. The shadow price represents the rate of change in the objective function value per unit increase in the right-hand side of the constraint, and for binding constraints, this value is often positive, indicating that relaxing the constraint would improve the objective function value.

Whenever a Constraint Has Negative Slack,the Shadow Price Is Zero