This study addresses cereal crop yield estimation as a probabilistic modeling challenge, highlighting the critical impact of underlying assumptions and distribution choices. Our primary objective was to develop a novel function for specifying and optimizing crop yield boundaries (lower l and upper g limits) using Grid-Search and Boundary Condition methods. The proposed methodology integrates an Evapotranspiration Production Function (ETPF)—modeled as a quadratic yield function—with a Crop Yield Index (CYI), thereby incorporating both agronomic and historical crop yield data. Using Teff yield data as a case study, we demonstrate how a generalized yield function can be mathematically reduced to maximum and minimum crop yield functions. The agronomic parameters and generalized function were estimated and validated by comparing the results from the Grid-Search and Boundary Condition approaches. The findings indicate that the final specification of a crop’s lower and upper yield limits is highly dependent on the specific interest and purpose of the model selection problem.