Abstract
In this research study Linear Programming (LP) Model is applied to determine the maximum profit from the three major crops (wheat, maize and alfalfa) in Central Yasin District Ghizer, where agriculture is the main source of income, however, due to population growth the agricultural land is used to construct buildings, which has minimized the land for agricultural use. In such a challenging condition a method to suggest the cultivation of a maximum profitable crop is the need of time. Therefore, LP model is an appropriate method to decide the profitable crop and to maximize the profit. The study was conducted employing quantitative method of research, with the purpose to compare the maximum profit per annum from the major crops, and to determine the beneficial crop among the three major crops in Central Yasin. All the farmers of the study area who grow the crops were the target population of the study and samples from the target population were selected using random sampling technique. Data was collected by conducting survey in the study area, where self-made questionnaires were distributed among the samples individually and responses were noted on the spot. The raw data is organized and analyzed using Microsoft Excel for LP model formulation. The result showed that the average land used for the cultivation of wheat, maize and alfalfa in the study area is 0.924 acres, 0.664 acres and 0.75 acres respectively. Furthermore, results of the LP model showed that alfalfa is the optimal solution rather than wheat and maize, and it (alfalfa) gives an average annual net profit of Rs.195634.488.
Highlights
Linear Programming (LP), is a sub-field of Optimization theory, which itself is a subfield of applied mathematics, is a class of mathematical problems, in which a linear function is maximized, subject to given linear constraints (Nakhanu, Toili, & Nyongesa, 2015)
Linear programming (LP) or Linear Optimization (LO) is an operations research technique which is widely used in finding solutions to complex managerial decision problems (Ezema & Amakom, 2012)
The optimal result obtained for allocation of land from the LP model is displayed in table 2
Summary
Linear Programming (LP), is a sub-field of Optimization theory, which itself is a subfield of applied mathematics, is a class of mathematical problems, in which a linear function is maximized (or minimized), subject to given linear constraints (Nakhanu, Toili, & Nyongesa, 2015). Model result suggested that tobacco and potato crops were part of the optimal solution which gained acreage by 128% and 38% respectively whereas maize and soya beans were not part of the optimal solution. Hassan et al (2004) designed linear programming model to optimize cropping pattern in Faisalabad Division, on wheat, basmati rice, IRRI rice, cotton, sugarcane, maize and potato. Singh et al (2001) cited by Hassan (2004), found that different water availability levels by applying LP model to suggests the optimal cropping patterns in the command of Shahi Distributary in Uttar Pardesh, India It is a common observation and practice that farmers in the study area grow crops, using the traditional ways and past experiences rather than experimental results or modern means. The present study was conducted to compare the maximum profit per annum from the major crops, and to explore the beneficial crop among the three major crops (wheat, maize and alfalfa) in the study area, using linear programming method
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