This study aimed at assessing different production functions for maize production in Tanzania. The maize yield performance, and agronomic – nitrogen use efficiency (AE) were evaluated under 6 rates of nitrogen (N) and water (W). Computations made for maize yield and AE shows that (i), the maximum potential maize yield increases with irrigation. (ii) less amount of fertilizer is needed to produce a unit of maize in the presence of high irrigation. Specifically, the maximum maize yield at 50 kg/ha of N is 6200 kg/ha and requires irrigation of 400mm, whereas at 100 kg/ha of N, the maximum yield is 5700 kg/ha and given 300mm of irrigation. Given the decrease in the fertilizer use efficiency, it implies that it is not plausible for farmers to apply optimum dose of nitrogen where there is water shortage. Moreover, two models, which are the quadratic function and the Mitscherlich-Baule function were fitted and compared based on a combination of agricultural, econometric and bioeconomic properties of the production process. The Mitscherlich-Baule function proved the best fit model. Results of the regression analysis shows that maize yield response to nitrogen (N) and water (W) exhibits diminishing returns. This suggests that when an extra unit of these input is added to the production process, less and less addition is observed in the total output. Based on the findings of this empirical study, it is plausible to recommend that farmers in the study area should be careful in applying the recommended dose of N where water is limited, because maize yield efficiency would not be maximized.