Production Mix Optimization in Small Manufacturing Enterprises Using Linear Programming: A Simplex Method Approach to a Packaged Snack Business

Abstract

Small manufacturing enterprises must balance market demand with limited production resources. Although linear programming has been increasingly applied in micro, small, and medium enterprises (MSMEs), evidence remains limited on snack-production models that jointly account for packaging materials, machine time, labor capacity, and demand constraints. This study sought to determine the optimal production mix and identify binding resource constraints at Plastik Sejahtera. A descriptive quantitative case study used data collected through direct observation, a structured interview with the business owner, and operational records from January to March 2026. The production mix was modeled using linear programming, solved through the simplex method, and verified using POM-QM for Windows. The optimal daily solution comprised 35 units of potato chips, 70 units of banana chips, and 100 units of oven-roasted peanuts, yielding a maximum modeled daily profit of Rp421,500. Machine time and labor capacity were binding constraints, while 13 kg of packaging capacity remained unused. These findings indicate that optimal production priorities depend on resource efficiency and demand limits alongside unit profit. The study illustrates how the simplex method can integrate operational constraints into production planning and provide quantitative decision support that complements small-business owners’ practical experience.