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Linear Programming 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. Likewise, linear programming is heavily used in microeconomics and business management, either to maximize the income or minimize the costs of a production scheme. Some examples are food blending, inventory management, portfolio and finance management, resource allocation for human and machine resources, planning advertisement campaign etc. Objective of Linear Programming Some objectives of linear programming are: (1) Identifying problem. (2) Formulation. (3) Solution. First we can define the problem or identified the problem. What is the actual problem? Second is to formulate a real life problem as a linear program is an art in itself. To aid you in this task, it is helpful to isolate the essential elements of the program as a means of asking what the clients want and what information be gained from the data that has been provided. The third stage is the solution of the problem. There are several method of finding the solution of linear programming. Such as Graphical method, simplex method, Big M method, the Two phase method etc. The use LP (Linear Programming) and Mississippi (Operational Research) in commercial packages. The Uses of Linear Programming and Operational Research in commercial packages: Operational Research in commercial packages as follows: Finance and investment: Developing the five year plan for a food manufacturer: Portfolio selection: Structure for the assets of a banks: Financing expansion of a small firm: Some of the major application areas to which Linear Programming can be applied are: Blending Production planning Oil refinery management Distribution Financial and economic planning Manpower planning Blast furnace burdening Farm planning Summary of Linear Programming Linear programming is a mathematical technique designed to aid managers in allocating scarce resources (such as labor, capital, or energy) among competing activities. Linear programming, sometimes known as linear optimization, is the problem of maximizing or minimizing a linear function over a convex polyhedron specified by linear and non-negativity constraints. Linear programming theory falls within convex optimization theory and is also considered to be an important part of operations research. Linear programming is extensively used in business and economics, but may also be used to solve certain engineering problems