Profit Optimization of Fajar Rohmah Rooftile Industry Using Linear Programming Simplex Method

This study aims to calculate the maximum profit from sales and assess the application of the simplex method in addressing raw material constraints in the production of Morando rooftiles, Palentong rooftiles, and bricks at the Fajar Rohmah Rooftile Factory. A quantitative approach was employed, using primary data collected through interviews with the factory owner in Ranji Kulon Village, Jatiwangi. Data processing and analysis were conducted using POM-QM for Windows software. The results indicate that the factory’s current production strategy is not optimal. An optimal profit of IDR 39,000,000 can be achieved by producing 18,000 Morando rooftiles and 4,125 bricks, while Palentong rooftiles are excluded from production. The study contributes theoretically by demonstrating the applicability of linear programming in optimizing industrial production under resource constraints. Practically, it provides a decision-making tool for production planning in SMEs. However, the study is limited to a single observation period and specific input constraints. Future research should incorporate sensitivity analysis and multi-period modelling to enhance the robustness and adaptability of the model across changing operational conditions.