Optimal Production Mix Determination for a Food Processing Company in Ogun State Using Linear Programming

Determining the optimal mix of products to manufacture is a foundational operations management problem for food processing companies operating under resource constraints. This study applies linear programming to identify the profit-maximizing production mix for a food processing company in Ogun State, South West Nigeria, that manufactures four categories of packaged food products. Data on contribution margins, machine time requirements, raw material consumption per unit, warehouse space, and monthly production capacity for each product category were obtained from the company's operations and finance departments. An LP model is formulated with the objective of maximizing total contribution margin subject to machine hour availability, raw material supply limits, minimum product output requirements, and storage capacity. The simplex method is applied to solve the model, and optimal output quantities are determined for each product category. Results indicate that the optimal product mix generates a monthly contribution that is 29 percent higher than the company's current production plan, primarily by shifting emphasis toward higher-margin product lines that make more efficient use of the binding machine time constraint. Shadow price analysis reveals that an additional hour of machine time yields N14,200 in additional contribution, indicating the high value of capacity expansion. Recommendations include targeted investment in additional processing equipment and a quarterly LP-based product mix review. This research provides accessible guidance for production planning in Nigeria's growing food processing industry. Keywords: linear programming, product mix optimization, food processing, Ogun State, contribution margin