Linear programming model for optimal crop allocation under varying land sizes in Pawaga, Tanzania

Farmers often rely on intuition when selecting crops, which can lead to suboptimal profits. In this study, we examine the optimal annual crop allocation under varying land sizes for farmers in Pawaga, Iringa District, Tanzania. A parametric linear programming (LP) model is developed to determine crop allocation combinations that maximise profit subject to land, labour, and capital constraints. Unlike conventional approaches that require separate models for different farm sizes, the proposed model accommodates land holdings ranging from 1 to 9 acres and integrates nine crop types within a single framework. Data were collected over three (3) agricultural seasons from extension officers and used to estimate production costs and returns. The model solution was obtained using linprog solver in MATLAB and presented in a graphical user interface (GUI). The results show that the optimal land size allocation for 9 acres of farm is 4.74 acres of Saro 5 and 4.26 acres of cassava, with an increased gross profit by 37% without increasing operating costs. A sensitivity analysis, conducted using Simplex LP Solver in Excel, confirmed the stability of the solution under moderate variations in key economic parameters. The results of the LP-based plans guarantees optimal yield as compared to traditional practice. The findings demonstrate that LP is a potential technique for practical decision-support and improved farm profitability