Application of Linear Programming to Profit Maximization.

This study applies linear programming to determine the profit-maximizing product mix for Seth Kojo's (S.K.) Bakery in Ghana. A mathematical model is formulated to allocate limited raw materials among four products: banana, coconut, wheat, and butter bread, subject to ingredient availability constraints. Using the linprog function in MATLAB, the model identifies the optimal monthly production levels and corresponding maximum profit. The results show that wheat and butter bread dominate the optimal solution, while coconut bread is excluded due to its inefficient resource-profit trade-off. The optimal mix yields a maximum monthly profit of GH¢407,350. Sensitivity analysis further reveals that butter- and flour-related constraints are binding, indicating that expanding these resources would generate the greatest marginal gains. The findings demonstrate the value of linear programming as a decision-support tool for small-scale enterprises and highlight how quantitative optimization can improve production planning, resource utilization, and profitability in bakery operations.