Lagrange Multipliers — Constrained Optimization

Optimize f(x,y) subject to g(x,y)=0. At the optimum, gradients are parallel: ∇f = λ∇g. The Lagrange multiplier λ measures how much the optimum changes per unit relaxation of the constraint — the "shadow price." Drag the constraint to see how the optimal point moves.

Contour Plot with Constraint

Lagrange Analysis