An analysis of a target system on a small-scale electron accelerator-driven system (e-ADS) for experimental purposes has been conducted. The methodology employed includes particle transport simulations using the Particle and Heavy Ion Transport System (PHITS) code and Response Surface Methodology (RSM) analysis performed with Minitab software. The independent variables reviewed are the energy and radius of the electron beam, as well as the thickness and radius of both the pitcher and the catcher. The dependent variable observed is the neutron yield. Tungsten is used as the pitcher material, while the catcher material is varied among iridium, platinum, tungsten, uranium, thorium, and lead. The RSM analysis indicates that the most optimal target system configuration is tungsten-tungsten, with a pitcher thickness and radius of 1.7 and 3.4 cm, respectively, and a catcher thickness and radius of 1.0 and 2.7 cm, respectively. To achieve the desired neutron output, the required beam parameters are a radius of 0.4071 cm, a current of 1 µA, and an electron energy of 100 MeV, respectively. This configuration produces a neutron yield of 5.764 × 1011 n/s, with a simulation deviation of 0.85%, which is considered acceptable for experimental purposes.