In this study, we discussed the functionality of transportation problem and regular simplex method then compared their run-time and optimized values with non-linear method called the Lagrange multiplier method. Lagrange multiplier is an algorithm that uses different mechanisms to choose the best optimal solutions. This method based on transforming the linear structure transportation problem into the nonlinear structure and solved it directly, by the techniques.We concluded that the computational results with a Lagrange method are better, easier and shorter than those with a specialized simplex method for large problems.