This study optimizes a biogas-fueled gas turbine-based cogeneration system designed for the simultaneous production of power, heating, fresh water, and hydrogen. Biogas is a sustainable alternative to fossil fuels due to its renewable and environmental benefits. Thermodynamic and exergoeconomic analyses using EES software evaluated the system's performance. The primary objective was to enhance performance by adjusting operational parameters through the Taguchi method. A Taguchi L27 orthogonal array optimized five control parameters across three levels, focusing on energy efficiency, exergy efficiency, and specific power production cost. The gas turbine inlet temperature emerged as the most critical optimization factor. Analysis of variance revealed that gas turbine temperature and air preheater temperature were the most influential parameters on energy efficiency, contributing 47.61% and 36.23%, respectively. Increasing the gas turbine temperature from 1150K to 1300K led to a 4.2$/GJ reduction in specific power production cost. The identified optimal conditions yielded a maximum energy efficiency of 83.72%, an exergy efficiency of 35.07%, and a minimum specific power production cost of 26.80$/GJ.