A Critical Review of the Application of the Simplex Method on Profit Maximization in Baker’s Cottage

This review critically examines the application of the simplex method for profit maximization in Baker’s Cottage as reported by Azman et al. (2022). The reviewed study formulated a linear programming model involving five bakery products and seven production resources and used Microsoft Excel Solver to identify a profit-maximizing product mix with a reported monthly profit of RM40,270.42. Although the study provides a useful practical demonstration of linear programming in production planning, this review identifies important analytical and interpretive limitations. In particular, the reported solution was presented as optimal without sufficient intermediate simplex information, such as a final simplex tableau or reduced-cost analysis, to permit independent verification. An independent simplex solution using ValuStats (VSP) 2.0 confirms the reported maximum profit and resource-slack values but reveals that the optimal allocation involves Chicken Floss, Spicy Floss and Frank Cheese rather than only Chicken Floss and Frank Cheese as emphasized in the original article. The review further demonstrates that water and sugar are the binding constraints, while flour, yeast, egg, milk and butter have substantial unused capacities. A supplementary case study illustrates how slack-variable values can provide additional information for resource-allocation and managerial decisions. The review concludes that simplex-based analysis should extend beyond the identification of an optimal objective value to include explicit optimality verification and meaningful interpretation of binding and non-binding constraints. Such an approach enhances the reproducibility, managerial relevance and decision-support value of linear programming applications.

Linear programming; simplex method; profit maximization; Baker’s Cottage; slack variables; resource allocation; Excel Solver; optimality.

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