Fused deposition modeling (FDM) is renowned as a prominent approach in the realm of 3D printing, where objects are built layer by layer using a heated nozzle to extrude melted materials. This research was conducted to identify the most effective FDM process variables to enhance tensile strength while simultaneously reducing surface roughness. Polylactic Acid (PLA) was chosen to fabricate test samples, showcasing the applications of 3D printing. In the course of this research, we conducted a series of 27 experiments to investigate the fundamental relationship between the parameters and the corresponding responses. An integrated approach for multi-objective optimization, combining grey relational analysis (GRA) with principal component analysis (PCA), was carried out to fine-tune three input parameters: printing speed, layer thickness and carbon deposition (C-deposition). The central aim of this study lies in optimizing the input variables for the technological manufacturing process of embossing parts in the context of Industry 4.0. Notably, experiment trial exhibited the highest grey relational grade (GRG), indicating optimal process parameter settings at printing speed of 100mm/s, layer thickness of 0.1mm, and C-deposition of 15mg respectively. The findings from this study can be utilized in various industries and applications where FDM 3D printing is employed.