Lagrange Multiplier Interpretation · Multivariable Calculus

Multivariable Calculus Quiz

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OPTIMIZATION IN SEVERAL VARIABLES

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For the problem: maximize

f(x,y) = 2\ln(x) + 3\ln(y)

subject to

x + 2y = 20

, the optimal solution has

\lambda = 0.4

. Two scenarios are considered: (A) changing the constraint to

x + 2y = 22

, and (B) changing the constraint to

x + 2y = 18

. The Lagrange multiplier interpretation predicts that scenario A increases the objective by 0.8 and scenario B decreases it by 0.8. Why might this approximation be less reliable for scenario B than scenario A?

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