In this study, a hybrid modeling approach combining first-principles equations with an artificial neural network was developed to reduce operating costs and carbon emissions in process utility systems of ethylene plant. The artificial neural network accurately predicted turbine power outputs under various operating conditions, with low maximum absolute percentage errors across all three turbines, demonstrating its ability to effectively capture nonlinear system behavior. The economic analysis showed that natural gas prices have a greater cumulative impact on operating expenses than the carbon tax due to their greater variability. Although the carbon tax has a higher local sensitivity, the steady increase in natural gas prices represents a persistent economic burden. This demonstrates the importance of managing fuel costs and monitoring changes in carbon policy to mitigate sudden increases in operating costs. With increasing output, the operating costs of the propylene and cracked gas turbines rose almost linearly, with the costs per megawatt rising more sharply for the propylene turbine. The ethylene turbine significantly impacted operating expenses despite lower output, showing small output changes can affect costs. Overall, the proposed methodology provides a reliable framework for optimizing energy performance, predicting fuel consumption and supporting operational decision in large-scale processes.