Assess students' ability to formulate and solve constrained optimization problems using Lagrange multipliers: construct the Lagrangian for functions of two or three variables with one or more equality constraints, solve the resulting system for critical points, interpret the meaning of the multipliers, and classify extrema (via second-derivative/constraint-based checks or direct comparison on the feasible set); include moderate algebraic problems and at least one case requiring handling degenerate or boundary scenarios and verification of solutions.