Application of Linear Programming in Profit Maximization: A Case of Selected Commercial Farms in Kalulushi District of Copperbelt Province, Zambia

Abstract

This study examined the application of linear programming in profit maximization in selected commercial farms in Kalulushi district, Zambia. The study was guided by three objectives which are; (a) To determine how linear programming models help farm management consultants work with their dairy farmer clients to develop improved pastoral-based dairy farm systems, (b) To determine the effectiveness and robust of the GSL linear programming model as an aid to dairy farm management decision making and (c) To suggest strategies which may encourage companies to adopt the application of linear programming technique in ensuring maximization of profit. A theoretical perspective undertaken for the present study is review of various different applications of linear programming. The population for this study consisted of Mathematics teachers as groups of individuals experiencing the teaching and learning at the selected school, workers at the selected farms and farm administrators giving a total of one thousand (1000). The distribution of the sample of 200 individuals among various categories was as follows:  Small scale local farmers (65), subject teachers of Mathematics (45), Government agricultural specialists (45) and farm administrators (55). Survey data is analyzed to determine the style of decision making and the problem is defined. The model equations with adequate restraints taking into account manufacturing limitations are solved using MS-Excel solver. Finally, the study found out that most farmers had no ideas about the use of the linear programming model in profit maximization at the farm. The study also discovered that some commercial farmers were using something close to the model but lacked enough knowledge to expand their ideas to get maximum results. To this effect, the study recommended that the government should deploy agricultural officers to educate the farmers on how well they can utilize their lands to make maximum profits.