Assess learners' ability to formulate and solve constrained optimization problems using Lagrange multipliers in business and engineering contexts. Include setting up the Lagrangian for single and multiple equality constraints, solving for stationary points algebraically, interpreting multipliers as shadow prices or marginal values, and applying second-order checks (e.g., bordered Hessian) where appropriate. Problems should require translating scenario descriptions (cost minimization, revenue maximization, resource allocation) into mathematical models, computing solutions, and explaining practical implications.