6. Optimization: equality constraints 6.1 Two variables, one constraint 6.1.1 Optimization with an equality constraint: necessary conditions for an optimum for a function of two variables 6.1.2 Optimization with an equality constraint: interpretation of Lagrange multipliers 6.1.3 Optimization with an equality constraint: sufficient conditions for a local optimum for a function of two variables 6.1.4 Optimization with an equality constraint: conditions under which a stationary point is a global optimum 6.2 Optimization with equality constraints: n variables, m constraints 6.3 The envelope theorem