Optimizing Agroforestry Systems: A Nonlinear Programming Approach

Abstract

Agroforestry integrates trees and crops in a symbiotic relationship, promoting sustainable agriculture. However, balancing the competing needs of these components is complex. This research develops a nonlinear programming framework to optimize agroforestry systems, considering factors such as crop yield, tree biomass, soil fertility, water use efficiency, biodiversity, and economic returns. The proposed model employs a weighted objective function to maximize overall system productivity while adhering to essential ecological and economic constraints. The optimal solution achieved demonstrates a crop yield of 120 kg/ha, tree yield of 100 kg/ha, soil fertility of 100 index units, water use efficiency of 70 liters/kg, biodiversity index of 80, and economic returns of $50/ha, with a maximum productivity and sustainability score of 93.5. This model serves as a valuable tool for agroforestry practitioners, providing a systematic approach to enhancing system performance and sustainability. The findings underscore the potential for optimizing agroforestry systems to achieve both high productivity and ecological resilience.