This study investigates inventory management and pricing techniques in a two-tier supply chain where newborn items are grown, slaughtered, and transported to retailers for consumer sale. This study assesses how certain carbon regulations can enhance or hinder profitability for suppliers and retailers, demonstrating the interdependence of their financial performance in connection to environmental regulations. A mathematical model considers demand as impacted by unit weight, selling price, and storage duration, with consumption patterns as a power function of these variables. This paper examines demand dynamics and proposes a solution for optimizing crucial factors such as the number of newborn items, the retailer’s selling price, and operating cycle time to increase profitability while maintaining excellent customer service.