Abstract
AbstractThis chapter focuses on linear programming and its application in agriculture, though appropriate non-linear and other variations such as separable programming, integer programming, goal programming and dynamic programming are described. The main purpose of the chapter is to explain what is meant by linear programming and how linear programming problems are solved on a computer. The emphasis of this chapter is on how a problem is translated into the mathematical conventions of linear programming. The use of a typical mathematical programming package is illustrated with specific reference to XPRESS-MP, and the mathematical concepts embodied in such a package are introduced. The process and conventions of mathematical formulation are illustrated by means of a case example, where a farmer wishes to determine the amounts of pig slurry and compound fertilizer to spread on 20 ha of grassland so that his total fertilizer costs are minimized. Also presented is a worked example of a farmer who wishes to formulate, as cheaply as possible, a rearing mix for feeding to his Hereford × Friesian steers which will satisfy certain nutritional requirements.
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