This paper presents an optimal sizing strategy for a hybrid generation system combining photovoltaic (PV) and energy storage systems. To achieve this, the optimization problem is solved using the simplex method for linear programming, implemented through Python. The model considers test data on electrical energy demand and solar irradiation, alongside battery operating conditions such as state of charge (SOC) and upper and lower charge limits as key decision variables. Conventional PV system sizing serves as a benchmark to assess the effectiveness of the optimization, with particular attention given to the computational resources required for problem solving.The results obtained from the optimization method demonstrate a substantial improvement in the utilization of energy resources, both from the photovoltaic system and the energy storage system. This approach enabled the design of an optimized system based on the proposed model, which was further refined using Matlab/Simulink.