Flow at minimum cost

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How do I find the minimum cost flow in a graph whose arcs have a lower and higher limit to the flow and a cost per unit of flow?

Note: Do not use linear programming. Initially there is no viable flow. Only the supply vertex is known. Suppose there will always be a viable flow of minimal cost.

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    Hi, Michael. Welcome back. That sounds like homework. Show what you’ve done and exactly where you’re having problems, otherwise it looks like you just want us to do your job for you.

  • This is a challenge of DIMACS for network flow http://lpsolve.sourceforge.net/5.5/DIMACS_mcf.htm. only that I want to solve without using simplex and its derivatives

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