Optimizing Fuel Production in Carbon Trading: A Karush–Kuhn–Tucker Framework for Sustainable Balance

This paper addresses the urgent challenge of climate risks amid escalating temperatures in 2023 and forthcoming projections for 2024. Focused on the intersection of climate risk mitigation, carbon trading, and the Karush–Kuhn–Tucker (KKT) optimization framework, we utilize advanced mathematical models to enhance emission reduction strategies within carbon trading systems. Our research emphasizes the dynamic interplay between production quantity, fuel prices, and the energy sector, aiming to contribute to both environmental impact and economic viability. The central exploration involves the application of the KKT model to navigate the intricate landscape of fuel production. Linear inverse demand functions are employed to quantify market demand and address relationships between fuel price and production quantity. The KKT model facilitates the definition and optimization of production quantities, balancing consumer needs, economic feasibility, and environmental impact mitigation. Integration of carbon trading mechanisms considers costs and benefits related to emissions reduction, achieving a delicate equilibrium between market demands and the carbon footprint of fuel production. A distinctive aspect of our approach is the direct inclusion of individual fuel producers into the optimization model, transforming profit objectives into refined KKT constraints for market equilibrium. This methodology signifies a substantial advancement in understanding and optimizing fuel production dynamics. Leveraging the KKT model, our research contributes valuable insights to sustainable energy practices, providing a theoretical foundation for academia and practical guidance for industry stakeholders navigating the delicate balance between economic prosperity and environmental responsibility.