Optimizing a Gourmet Canned Foods Production

In mathematics, linear programming (LP) problems are optimization problems in which the objective function and the constraints are all linear. Linear programming is an important field of optimization for several reasons. Many practical problems in operations research can be expressed as linear programming problems. Certain special cases of linear programming, such as network flow problems and multicommodity flow problems are considered important enough to have generated much research on specialized algorithms for their solution. A number of algorithms for other types of optimization problems work by solving LP problems as sub-problems. Historically, ideas from linear programming have inspired many of the central concepts of optimization theory, such as duality, decomposition, and the importance of convexity and its generalizations. (wikipedia.com) Linear programming (LP) is one of the most widely applied O.R. techniques and owes its popularity principally to George Danzig's simplex method (Danzig 1963) and the revolution in computing. It is a very powerful technique for solving allocation problems and has become a standard tool for many businesses and organisations. Although Danzig's simplex method allows solutions to be generated by hand, the iterative nature of producing solutions is so tedious that had the computer never been invented then linear programming would have remained an interesting academic idea, relegated to the mathematics classroom. Fortunately, computers were invented and as they have become so powerful for so little cost, linear programming has become possibly one of the most widespread uses for a personal PC. (wikipedia.de) There are of course numerous software packages which are dedicated to solving linear programs (and other types of mathematical program), of which possibly LINDO, GAMS and XPRESS-MP are the most popular. All these packages tend to be DOS based and are intended for a specialist market which requires tools dedicated to solving LPs. In recent years, however, several standard business packages, such as spreadsheets, have started to include an LP solving option, and Microsoft Excel is no exception.