The purpose of this study is to compare the relative superiority between linear programming theory, which has been traditionally used as a decision-making tool, and the theory of constraints, whose importance has been increasingly growing in recent years. Specifically, because existing studies comparing the two theories with a focus on product mix problems have failed to clearly present the criteria for comparison, this study established comparison criteria such as logical validity, superiority of derived solutions, and scope of practical application to overcome the shortcomings of existing research, and compared the two theories under these criteria. To achieve the research objective, three scenarios were used to compare and analyze the two theories, with each scenario incorporating a decrease in production capacity and demand, a demand increase due to price changes, and an increase in production capacity through overtime, respectively. The research results indicated that because the theory of constraints focuses on only one constraint at a time rather than simultaneously considering multiple constraints in decision-making, it has the potential to present inferior solutions compared to linear programming theory. Moreover, in the process of deriving solutions for various scenarios, the theory of constraints did not provide greater ease of problem-solving than linear programming theory. However, in certain decision-making situations such as the determination of overtime hours addressed in this example, the superiority of the theory of constraints solution versus the linear programming solution varied depending on the values taken by special variables such as hourly overtime wages.