The article presents the results of the technical–economical study regarding the optimization of fused deposition modeling (FDM) parameters (the height of the layer deposited in one pass—Lh and the filling percentage—Id) for the manufacture of Polyethylene Terephthalate Glycol (PETG) and Acrylonitrile Styrene Acrylate (ASA) parts. To carry out this technical–economical study, was used the fundamental principle of value analysis, which consists of maximizing the ratio between Vi and Cp, where Vi represents the mechanical characteristic, and Cp represents the production cost. The results of the study show that for tensile specimens made of PETG, the parameter that significantly influences the results of the Vi/Cp ratios is the height of the layer deposited in one pass, (Lh), and in the case of the compression specimens made of PETG, the parameter that significantly influences the results of the Vi/Cp ratios is filling percentage (Id). In the case of specimens manufactured via FDM from ASA, the parameter that decisively influences the results of the Vi/Cp ratios of the tensile and compression specimens is the filling percentage (Id). By performing optimization of the process parameters with multiple responses, we identified the optimal parameters for FDM manufacturing of parts from PETG and ASA: the height of the layer deposited in one pass, Lh = 0.20 mm, and the filling percentage, Id = 100%.