Batteries have been a forefront energy storage solution owing to their flexibility to supply power to a broad range of applications. Lithium-polymer (LiPo) batteries, a subcategory of the widely adopted lithium-ion batteries, exhibit heightened safety properties due to the utilization of a solid or gel polymer that acts as a separator and electrolyte. In this study, a pseudo-2D electrochemical coupled thermal multiphysics model of lithium cobalt oxide (LCO) cathode, graphite anode, and poly(vinylidene fluoride-hexafluoropropylene) (PVdF-HFP) polymer electrolyte LiPo battery was developed using COMSOL Multiphysics®. To improve the model accuracy and battery performance, ten parameters for energy density optimization were screened via sensitivity analysis, and the five most sensitive parameters were selected for optimization. Simultaneous optimization of these parameters through the Constrained Optimization By Linear Approximation (COBYLA) optimization algorithm resulted in a ~25 % increase in energy density and a ~21 % increase in power density for both 1 C and 0.5 C discharge rates without significantly increasing heat generation during discharge. These increases are attributed to the maximization of anode active material and the minimization of electrode and separator thicknesses. The developed model can be integrated into the experimental design of batteries to improve target performance applications such as energy and power. It can be further employed to optimize various battery chemistries and configurations.