Optimization of Cobb-Douglas production functions

The purpose of this research is to know simultaneously from the influence of working capital, land area and labor. This analysis uses descriptive quantitative research methods. The data used is secondary data from the research conducted by Suryati. The data were analyzed using the Cobb-Douglas production function and estimated its parameters using Gauss Newton-Nonlinear Least Square. the optimum production function can be obtained by minimizing the function constraints, therefore the Lagrange method is used to obtain the minimum constraint function. In the results of the research it was found that the input elasticity of land area and labor affected production output. Model of Cobb-Douglas production function in onion production in Sakuru Village, Monta District, Bima Regency is $\hat{{\rm{Q}}}=5,305,000{\,{\rm{x}}}_{1}^{0.5957}{\,{\rm{x}}}_{2}^{0.0766}$. The maximum production can be achieved with a land area of 13.19 acres and a workforce of 6 people.