Application of Linear Programming to Resource Allocation in Small-Scale Businesses in Onitsha, Anambra State

This study examines the application of linear programming models to resource allocation challenges confronting small-scale businesses in Onitsha, Anambra State, South East Nigeria. Small enterprises in this commercial hub frequently operate under constrained budgets, limited labour supply, and fluctuating raw material availability, making optimisation an urgent practical concern. Drawing on recent advances in operations research and management science, the study formulates linear programming models tailored to the operational realities of selected businesses in the Onitsha Main Market and its environs. Data are collected through structured questionnaires administered to fifty business owners, supplemented by direct observation of production and distribution processes. The simplex method is applied to solve the formulated models, and sensitivity analysis is conducted to assess the robustness of optimal solutions under varying input conditions. Findings indicate that a significant proportion of surveyed businesses allocate resources sub-optimally, resulting in measurable losses in output and revenue. The study demonstrates that even simplified linear programming frameworks can yield substantial efficiency gains when properly implemented by small enterprise operators. Recommendations are offered for the integration of basic quantitative methods into business planning curricula at vocational and tertiary institutions in the South East zone. The study contributes to the growing literature on applied mathematics in informal and semi-formal economic settings in Nigeria, and provides a replicable methodological template for similar investigations in other commercial centres across the country. Keywords: linear programming, resource allocation, small-scale businesses, simplex method, Onitsha