In light of growing awareness surrounding carbon emissions, companies are urged to integrate sustainability into their conventional inventory systems, aligning both monetary and environmental goals. Regulatory policies aimed at reducing carbon emissions have significantly impacted profit-driven enterprises. So, the proposed research delves the complex interplay between inventory management, carbon emissions, partial backlogging, price-stock-dependent demand, and deterioration within a unified framework. In this article, the authors propose a comprehensive model that accounts for these factors simultaneously, aiming to optimize inventory decisions while minimizing environmental impact and meeting customer demand. The model considers the carbon emissions associated with inventory holding and transportation, highlighting the significance of sustainable practices in managing supply chains. Additionally, partial backlogging is incorporated to reflect situations where only a portion of unfilled demand is satisfied in subsequent periods, enhancing the realism of the model. Moreover, we incorporate the impact of both price and stock levels on demand, acknowledging their dynamic nature in shaping consumer behavior. Deterioration is another critical aspect considered in the model, recognizing the natural decay of perishable goods over time. The authors employ mathematical optimization techniques to derive optimal policies for inventory replenishment, order quantities, and pricing strategies, considering both economic objectives and environmental sustainability goals. Numerical experiments are performed to demonstrate the efficacy of the proposed model in achieving a balance between competing objectives and to offer insights into the trade-offs involved in sustainable inventory management practices.