Intangibility of knowledge and unclear relationship between inputs and outputs has caused difficulties in knowledge production control. In this paper we present a model to clarify the relationships between inputs and outputs in knowledge production and develop knowledge production functions. In order to accomplish this, we extract resources of knowledge production and product utility indices from the literature. In order to develop production functions, we apply Analytical Hierarchy Process (AHP) to find the weights of production factors for each utility index and establish linear production functions by AHP results. Then, with the practical data and applying gradient descents method, we improve the coefficients of the linear functions. A set of data is generated through the linear functions. A neural network is then trained by this set of data and gathered data from the case to find the relationship of utility indices and production factors. So, we improved the production functions by real data. We applied this method in Ghods newspaper office. Although the t test verifies the performance of our method, the gradient descents method and neural network method decrease the mean square error.