Optimizing production planning problems is often defined by conflicting objectives, such as minimizing costs, maximizing benefits, and meeting product quantity requirements under uncertainties and within fuzzy environments. To overcome these challenges, the fuzzy goal programming (FGP) model was applied. The FGP model can compromise between objectives to achieve optimal membership functions of each objective while simultaneously maximizes the overall achievement function. Moreover, the FGP model was applied to optimize the production planning problem in a realistic case study from the packaging industry. There are eight different objectives and two hard constraints. These objectives involve profitability, costs, and the minimum requirements for each product, allowing for some tolerance. However, cycle time and material usage must strictly adhere to the specified requirements. The results showed that the proposed FGP model effectively optimizes the production planning problem by determining the optimal quantities of each product to be produced and calculating the membership function values for each objective. The model ensures the highest possible overall membership function while strictly satisfying all the production constraints. Moreover, the proposed model was further analyzed under various parameter scenarios reveals that certain objectives probably exceed production capabilities and thus be unachievable in practice. This analysis provides a clearer understanding of feasible operational boundaries. The contributions of this study can be generalized to other industries facing similar multiple goals and uncertain conditions, making it a versatile tool for production optimization.