Application of Linear Programming to Optimize Production and Profit (A Case Study of Oda Natural Spring Water Factory)

This research focuses on optimizing production processes at Oda Natural Spring Water Factory in Ethiopia through the application of Linear Programming (LP). In the competitive bottled water industry, efficient resource management is crucial for profitability. Oda Natural Spring Water, known for its unique selenium-rich composition, faces challenges related to inefficient production practices and suboptimal resource allocation. This study develops a tailored LP model to determine the optimal daily production quantities for four bottled water sizes (35cl, 60cl, 100cl, and 200cl), with the objective of maximizing profit while adhering to constraints such as production time, cost budget, and market demand limits. Data collected over six months were analyzed using Excel Solver. The findings indicate that the factory can achieve a maximum daily profit of 150,143 Ethiopian Birr (ETB) by producing 1,100 packs of 35cl, 1,714 packs of 60cl, 1,441 packs of 100cl, and 976 packs of 200cl water. Sensitivity analysis reveals that the production cost constraint is binding, while significant production time remains unused. The study underscores LP as a practical decision-making tool in manufacturing, providing actionable strategies for improving resource allocation, reducing costs, and enhancing profitability. Recommendations include cost reduction initiatives and regular review of production plans in response to market dynamics.