PEMECAHAN MASALAH NONLINEAR PROGRAMMING DENGAN LAGRANGEAN METHOD MENGGUNAKAN SUBSTITUTION METHOD ATAU MICROSOFT EXCEL

Lagrange Multipliers are a mathematical tool for constrained optimization of differentiable functions. The given procedure defines the Lagrangean Method for identifying the stationary points of optimization problems with equality constraints; L(λ,X) = f(X) – λg(X – C). This function is called the Lagrangean function and the parameters λ is the Lagrange Multipliers. The partial derivatives of this equation ∂L/∂λ = 0 and ∂L/∂X = 0 will give the optimal result for X.\ud \ud However, in some cases, sometimes we have been facing some difficulties to solve nonlinear programming problem with this method, therefore we would like to introduce the Substitution Method or Microsoft Excel Method, which is simple, easier and faster to solve the nonlinear programming problem. Because of the mathematical nature of nonlinear programming models, and in management science we do not have a single general technique to solve all mathematical models that can arise in practice, therefore simpler approaches should be explored first. In some cases, a “common sense” solution may be reached through simple observations.\u