Abstract
This study investigates how linear programming can be effectively applied to optimize raw material usage in the bakery industry, with the aim of maximizing profit while adhering to resource constraints. Given that raw materials account for a significant portion of production quality and cost, this study focuses on the strategic allocation of limited raw materials at Double 4 Bakery in Bauchi, Nigeria. A quantitative approach was adopted, utilizing linear programming techniques to develop a mathematical model for profit maximization. Data on raw material availability and cost-profit contributions of three bread sizes—small, big, and family loaf—were collected through secondary sources. The model was analyzed using the simplex method via LINGO software to determine the optimal production mix. The analysis revealed the optimal quantities of each bread size that should be produced to maximize profits while staying within the limits of available raw materials. Specifically, the study showed how each bread type's contribution margin and resource consumption interact to influence the optimal solution. The model helped identify the most profitable product combination, validating the efficiency of linear programming in resource allocation and decision-making. The study provides bakery managers and production planners with a practical tool for optimizing production decisions, reducing waste, and maximizing returns. By implementing the recommended production plan, bakeries can enhance operational efficiency, better manage raw material inventories, and improve profit margins under varying market and supply conditions. This research contributes to the growing body of literature on operations research applications in small-scale manufacturing, particularly in the bakery industry in Nigeria. It offers a context-specific model that can be adapted by similar enterprises seeking to enhance profitability through scientific decision-making techniques. The case-based approach demonstrates the real-world applicability of linear programming to solve complex production challenges.

Key words: Optimization, Bread, Linear Programming, Simplex method, Lingo Software