[Assess students' ability to apply Lagrange multipliers to find and classify extrema of functions of several variables subject to one or more smooth equality constraints. Scope includes forming the Lagrangian, solving ∇f = Σ λ_i∇g_i systems, handling multiple constraints and degenerate cases, eliminating variables or solving algebraic systems as needed, and verifying/classifying candidate points (including checking boundaries or second-order conditions where applicable). Problems require clear setup, solution of the resulting system, and justification of which solutions are maxima, minima, or saddle points.]