APPLICATION OF LINEAR PROGRAMMING IN PRODUCTION OPTIMISATION USING SIMPLEX METHOD: A CASE STUDY OF MAIZUBE FARM LIMITED
DOI:
https://doi.org/10.33003/fjs-2026-1003-4823Keywords:
Linear programming, Simplex method, Optimal solution, Feasible solution, OptimisationAbstract
Efficient allocation of limited production resources is a major challenge faced by manufacturing and agro-processing industries seeking to maximise profit. This study examines the application of linear programming techniques in optimising production decisions at the dairy section of Maizube Farm Limited, with emphasis on the production of three yoghurt products: Big Yoghurt, Medium Yoghurt, and Small Yoghurt. The study investigates how available resources such as labour, production time, and raw materials can be optimally allocated among these products to achieve maximum profitability. A linear programming model was formulated to represent the production system, with profit maximisation as the objective function and production constraints reflecting the limited availability of key resources. The formulated model was solved using the Simplex tableau method, which iteratively evaluates feasible solutions until the optimal production plan is obtained. The results show that the optimal solution was obtained at the first tableau iteration with (X2= 5.5), yielding a maximum profit value of (Z=12,100). The results demonstrate the effectiveness of linear programming as a decision support tool for optimising production planning and improving resource utilisation in dairy processing operations. The study therefore highlights the practical relevance of mathematical optimisation techniques in enhancing productivity and profitability in agro-industrial systems.
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