A cash crop combination for maximum net income: A case study of a small-scale cash crop farmer in Vhembe, Limpopo province, South Africa

This paper investigates the optimal cash crop combination at a small-scale cash crop farm in Vhembe District, Limpopo Province, South Africa in which green maize, cabbages, tomatoes, spinach, mustard, butternut and sweet potatoes are grown. To get optimum farm outputs, decisions on crop combination and operational activities in crop production are crucial. Proper farm planning and resource allocation play a significant role in optimising farm revenues. It was observed that the farmer used traditional methods of allocating resources, which lead to a less profitable crop mix. In view of this, in this study, linear programming model was formulated using data collected from a farm concerning the past crop combinations and allocation of resources in crop planning and production to determine the best crop combination that maximizes net income given limited resources such as land, labour, capital, and others. The simplex method of linear programming works by first locating a feasible solution and then relocating to any vertex of the feasible set that improves the cost function. Eventually, a point is reached beyond which no further movement improves the cost function. The results of the developed linear programming model were compared to past farming practices based on experience, leading to the conclusion that crops and limited resources were not optimally allocated. The results clearly demonstrate the optimal crop combination and allocation of scarce resources that the farm could have considered to yield maximum returns. It is observed that the proposed linear programming model is appropriate for finding the optimal land allocation criteria for the cash crops in the study area. The optimal crop mix from the linear programming two phase simplex method show that the farmer should grow the following crop mix, 1.16 ha of green mealies, 2.64 ha of cabbages, 0.8 ha of tomatoes, 1.2 ha of mustard, 0.4 ha spinach, 0.4 ha of butternut and 0.4 ha of sweet potatoes with the gross income of R 740 800. The linear programming model resulted in a 37.8 percent increase in profit margin. Based on the results obtained from this study, it is recommended that the small-scale cash crop farmer should invest more in producing crops that give maximum profit. MATLAB software was used to determine the optimal values of the decision variables.