The method of Lagrange multipliers is a very useful and powerful technique in multivariable calculus. In this paper interpretation of Lagrange multipliers is given by showing their positive values. Three models on optimization are given with detailed mathematical calculations. The Implicit Function Theorem is important for solving a system of non-linear equations for the dependent variables and calculating partial derivatives of these variables with respect to the independent variables. In this paper an attempt has been made to optimize economic models subject to a budget constraint, using Lagrange multipliers technique, as well as, using necessary and sufficient conditions for optimal value.