Livestock production companies come under increasing responsibility to reduce their environmental impact, and thereby, the simultaneous decision-making of inventory replenishment and emissions reduction investment has become essential for ensuring sustainable development in the livestock farming business. This study investigates, for the first time, the best investment strategy for a livestock farming business under the carbon cap (CC) environmental legislation, taking into account both the edible and non-edible parts of slaughtering mature growing items (GIs) after procuring and feeding baby GIs. By fusing economic and environmental factors, this study aims to shed light on two crucial issues: (i) figuring out the appropriate level of investment needed for the farm to adhere to the CC environmental regulation; and (ii) evaluating the effect of the investment decision on the farm's expenses and emissions levels. To deal with these insights, a thorough analytical framework integrating mathematical modeling methodology, economic evaluation, and carbon accounting approaches is employed. By analyzing the interaction between the farm's emissions reduction investments and replenishment choices, the cost-effective investment level is determined that enables the farm to satisfy the carbon cap obligation while guaranteeing maximum operational efficiency. The results of this study have important ramifications for livestock farming businesses trying to make their way through the stringent CC emission law. The results indicate that in order to keep the business feasible when the cap of the CC guideline is low, the livestock-producing farm should give priority to investing in minimizing feed emissions and using cutting-edge manure treatment methods.