Optimizing Profit-to-Cost Ratios in Bakery Production Using the Hasan–Acharjee Fractional Programming Method - Fahliza Adisty; Riri Syafitri Lubis (Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang, 2025)
Production optimization under resource constraints can be effectively modeled using Linear Fractional Programming (LFP), where the objective function is defined as a profit-to-cost ratio. This study applies the Hasan–Acharjee method to optimize production planning in a household-scale bakery enterprise in Indonesia, considering four product types and three resource constraints (materials, labor, and equipment). The model was reformulated as a single linear program and solved using LINGO 21.0. Validation against the classical Charnes–Cooper transformation confirmed identical optimal solutions, demonstrating the robustness of the Hasan–Acharjee approach. Sensitivity and trade-off analyses further revealed how variations in costs and production capacity influence profitability. The results highlight both the theoretical relevance of the Hasan–Acharjee method in fractional programming and its practical applicability to small and medium-sized enterprises seeking efficient resource utilization under limited conditions.