Applied Mathmatics

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The use of linear programming in economics
The use of linear programming in economics

Linear programming is the process of taking various linear inequalities relating to some situation, and findinag the "best" value obtainable under those conditions. A typical example would be taking the limitations of materials and labor, and then determining the "best" production levels for maximal profits under those conditions. In "real life", linear programming is part of a very important area of mathematics called "optimization techniques". This field of study (or at least the applied results of it) are used every day in the organization and allocation of resources. These "real life" systems can have dozens or hundreds of variables, or more. In algebra, though, you'll only work with the simple (and graphable) two-variable linear case.

It can be applied to various fields of study. It is used in business and economics, but can also be utilized for some engineering problems. Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing. It has proved useful in modeling diverse types of problems in planning, routing, scheduling, assignment, and design.

Linear programming is a method of economic and business analysis that relies on matrix algebra and other mathematics techniques to achieve the highest level of satisfaction -- maximum profits, for example -- subject to a set of known constraints. The challenge of maximizing satisfaction within a set of limits makes linear programming an ideal tool of analysis for economics, which studies the ways in which households, businesses and societies allocate limited resources to achieve needs and wants. In economic analysis, linear programming has broad applications in industrial management and operations. Managers of industry want to maximize their companies' profits or minimize production costs, but recognize the existence of constraints. For example, managers of an...
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