Using Linear Equations Approach to Formulate Balanced and Least-Cost Ration for Dairy Cattl

Abstract

Abstract The main objective of this study was to find an effective way to use linear equations for the purpose of creating a balanced ration at the lowest possible cost for dairy cattle by using linear equations and solving these equations through the Solver tool provided by MS-Excel. Samples of barley, corn, wheat bran, soybean meal and wheat straw were collected from the local markets and the necessary chemical analyzes were performed for them. after that the mathematical formulas of the linear equations were developed according to the specified constraints for crude protein ratio, value of metabolizable energy and the percentage of each calcium and phosphorus, which meets the needs of a medium-production dairy cow (15 kg) and weighting (650 kg). then the data was entered into Microsoft Excel and the equations were solved by Solver tool. The results showed a superior ability of linear equations to solve the problems consisting of several variables where the feed was formed by mixing barley, Corn, wheat bran, soybean meal, wheat hay, calcium phosphate and salt in proportions ( 5, 17.91, 50, 10.76, 13.66, 1.64 and 1) respectively, The cost of the feed mixture was (268.6 $/ton), which is the lowest possible cost for a ration that meets the required needs, linear programming will provide the animal breeders efficiency with the highest production by reducing the costs and balancing of the ration through the steps described in the search.