Abstract
Background: Many Libyan manufacturing companies rely on intuitive decision-making, leading to suboptimal resource allocation. Objective: This study applies linear programming (LP) to optimize production portfolio and maximize monthly profit in a Libyan beverage company. Methodology: A case study was conducted using data for four products (two bottled waters, two juices) subject to production time (12,000 minutes/month), water availability (100,000 L), raw material budget (60,000 LYD), and demand limits. The LP model was solved using Excel Solver. Results: The optimal solution recommends producing 4,000 units of large bottled water (1.5 L) per month and zero units of all other products, yielding a maximum monthly profit of 6,400 LYD. Production time is the only binding constraint (shadow price = 0.533 LYD/minute). The LP solution outperforms intuitive diversification by 18.5% and highest-margin heuristics by 30.6%. Conclusion: Per-unit profit margin is misleading; profit per constraint is the correct metric. Libyan managers should adopt LP using accessible tools like Excel Solver to improve production decisions.
Keywords: Linear Programming; Production Optimization; Operations Research; Decision Making; Libyan Industry; Case Study; Excel Solver; SMEs; Developing Countries.