The Lagrange multiplier at the optimum gives only the instantaneous rate of change in the objective value.

Name: The Lagrange multiplier at the optimum gives only the instantaneous rate of change in the objective value.
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The Lagrange multiplier indicates the rate of change of the objective function with respect to a constraint, reflecting the sensitivity of the objective value to changes in the constraint at the optimum.

The Lagrange Multiplier at the Optimum Gives Only the Instantaneous