Use of the Chebyshev Polynomial Approximation in the Analysis of Milk Production and Average Weight at Birth Calves Depending on the Volume Food and the concentrate

Abstract

In this study published the influence of two nutritional factors of milk production and the use of the production functions in the farming sector. The production, profit, and management are key elements for efficient economy. The main purpose of the project is to use contemporary methods for economic analyses of the use of resources (inputs), more specifically in small family farms. Nowadays in order to have a sustainable development of the agricultural farms, especially the livestock farms, it requires an economic optimization, as well as continuous analyses of economic and technical of influential factors. The main method used on the above mentioned study is the ones of Cobb-Douglas production function. This method analyses the impact of nutritional factors (the structure of the nutritive ration; wet, dead, concentrate) on bovine milk production. As illustrated in the article the economic theory combined with the deep mathematic logic are two main directions for the treatment of production functions. The study was conducted in ‘’Agrotex’’ farm in Lushnje district. They were processed and analyzed data on the feeding phase and data on milk yield and weight of calves at birth for a period of 5 years. They were processed and analyzed data feeding phases mentioned above and milk yield and weight of calves at birth. These data were analyzed for a period of 5 years (period 2008-2012) with a number of heads of: 103, 111, 176, 118, 139 respectively in 2008, 2009, 20010, 20011, 2012.During the study is used Cobb-Douglas production function to analyze the impact of two components ration on milk production and approaches in the Chebishev's polynomials to solve systems of constraints. It appears that the most appropriate structure of the ration, to provide an average yield of 6478.3 kg milk / lactation (305 days), or an average of 21.3 kg milk / day, should be as follows: 17558.7 kg voluminous food and = 2265.7 kg concentrate. We prove that maximum profit and minimum cost to achieve food = 17558.7 kg = 2265.7 kg voluminous and concentrated. In this case the amount of milk produced by a cow will be 6478.3 kg while the average weight of calves at birth will be 43.8 kg. This study confirms that balanced nutrition is the primary factor in increasing economic efficiency of farms. As a result, the study demonstrates that the maximum profits, as well as the maximum income, are reached at the same point in the expansion path, where the cost is minimal.

DOI: 10.5901/mjss.2013.v4n9p660