Assess students' ability to apply the method of Lagrange multipliers to locate and classify constrained extrema of multivariable functions: set up and solve the Lagrangian for problems with one or more equality constraints, solve for multipliers and variables, interpret solutions (including feasibility and multiple candidate points), and use appropriate second-order tests or bordered-Hessian reasoning; include geometric and applied optimization examples (e.g., area/volume, distance, cost) and note how to handle degenerate or boundary cases.