The extended mathematical programming Model (ENLPM) is presented here as a new tool to study both regression (for nonlinear – in – the – parameter estimation) rule and optimal decision making problems simultaneously, using an experimental wheat production data. Initially, the essentials of the new technique introduced in this paper are outlined for the estimation of the nonlinear coefficients of a polynomail biological production function as compared with other numerical search methods (Gauss – Newton Algorithm); secondly, the extended model is provided with an endogenous variable k as the degree of nonlinearity of parameters for making sensitivity analysis to test the validity of many different nonlinear – in – the – parameter statistical models. Thirdly, the estimated nonlinear parameters along with product and input prices are used to provide necessary information regarding the input variable cost and supply functions for the underlying nonlinear – in – the – parameters biological production function for the crop of wheat . The main results indicate that the extended mathematical programming model (ENLPM) can be used as an alternative method for nonlinear least squares estimation. The objective in this nonlinear estimation is to locate the global minimum of the function of sum of squared error terms, Given the estimated nonlinear parameters, the determinant of Hessian is used for the validity of a convex objective function.
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