The purpose of this investigation was to design an optimal production plan for a soft drink bottling plant located in San Jose de Cucuta (Colombia), where the productive system's constraints were identified to develop a mathematical model following the operations research methodology, specifically the linear programming technique, together with the theory of constraints. As a result, the optimal quantities of manufacturing were obtained at the lowest cost for the selected period (June, 2011). Besides, the study also allowed us to identify an unused productive capacity, from which scenarios and opportunities were identified to use their resources. The mathematical model that represents the optimal production plan could be implemented in soft drink bottling plants that have the same characteristics of the case study considered in this article.