Application of Linear Programming to Crop Allocation in Smallholder Farms in Benue State

This study investigates the application of linear programming (LP) techniques to optimize crop allocation among smallholder farmers in Benue State, located in Nigeria's North Central geopolitical zone. Agricultural productivity in this region has remained constrained by inefficient land use, limited capital, and poor resource allocation practices. Drawing on data collected from 120 farming households across three local government areas, the study formulates an LP model that maximizes farm income subject to constraints including land area, labour availability, water access, and seed capital. The simplex method is employed to solve the optimization problem, and sensitivity analysis is conducted to assess the robustness of the optimal solution under varying input costs. Findings indicate that current allocation patterns deviate significantly from the LP-recommended optimum, resulting in an estimated 34 percent loss in potential income. The model suggests that reallocating land toward a combination of soya beans, maize, and yam, guided by seasonal price indices, can substantially improve household earnings. This study contributes to local agricultural planning by providing a reproducible, data-driven framework that extension officers and cooperative societies can adopt. Recommendations include integrating LP tools into the State Agricultural Development Programme and training field officers in model interpretation. The research affirms the practical relevance of operations research methods in addressing food security challenges within Nigeria's agrarian communities. Keywords: linear programming, crop allocation, smallholder farming, Benue State, simplex method