In this study, the influence of specific 3D printing parameters, including layer thickness, nozzle diameter, and infill density, on the mechanical properties of parts fabricated via Fused Deposition Modeling (FDM), specifically ultimate strength and impact energy, was investigated. Based on input parameters at three levels and experimental design using the Response Surface Methodology (RSM), 17 samples were printed for tensile and Charpy impact testing. Following the extraction of results for the aforementioned responses, mathematical modeling was conducted to fit the outputs and analyze the interaction of each input on the problem's responses, ultimately determining the optimal parameter settings. The results indicated that the developed modeling provides a suitable prediction of the impact of input parameters on output responses. Furthermore, increasing the layer thickness exhibited the most significant effect on the output responses compared to the other two parameters. Conversely, unlike the equivalent ultimate strength force, where increasing infill density and nozzle diameter does not necessarily lead to an increase in its value, increasing any of the printing parameters results in enhanced impact energy. While the maximum Charpy impact energy (1.16 J) and the maximum equivalent ultimate strength force (1299.3 N) were recorded in different samples, the optimal parameter selection for maximizing both ultimate strength force (1 kN) and Charpy impact energy (1.16 J) simultaneously corresponds to a sample with a layer thickness of 2 mm, nozzle diameter of 0.5 mm, and infill density of 50%.