As the issue of global climate change becomes increasingly severe, governments worldwide have implemented carbon reduction policies, such as carbon taxes and industrial low-carbon transitions, to effectively control total carbon emissions. This study applies a multi-objective programming approach and uses the plastic raw material manufacturing process in the petrochemical industry as an example to explore how companies can balance profit maximization with minimizing production-related carbon emissions. By integrating Activity-Based Costing (ABC) and the Theory of Constraints (TOC), this study develops a production decision-making model and employs the ε-constraint method to impose carbon emission constraints, analyzing the resulting changes in corporate profitability. The model considers three different policy scenarios: basic carbon tax costs (including the use of renewable energy), continuous incremental progressive carbon tax costs, and discontinuous incremental progressive carbon tax costs. The results indicate that adopting renewable energy effectively reduces carbon emissions during production, while the discontinuous incremental carbon tax model provides better control over emissions. Under different carbon emission constraints, significant variations in optimal profits and production volumes are observed across the models, offering valuable insights for governments and enterprises in formulating carbon reduction strategies.