# Research Paper On Linear Programming

The Graph is a powerful mathematical tool applied in many fields as transportation, communication, informatics, economy, … In an ordinary graph, the weights of edges and vertexes are considered independently where the length of a path is... more

The Graph is a powerful mathematical tool applied in many fields as transportation, communication, informatics, economy, … In an ordinary graph, the weights of edges and vertexes are considered independently where the length of a path is the sum of weights of the edges and the vertexes on this path. However, in many practical problems, weights at a vertex are not the same for all paths passing this vertex but depend on coming and leaving edges. The presented paper develops a model of the extended linear multi-commodity multi-cost network that can be more exactly and effectively applied to model many practical problems. Then, maximal limit cost flow problems are modeled as implicit linear programming problems. On the base of dual theory in linear rogramming, an effective approximate algorithm is developed.

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