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Help on a math problem.

In the example below we have one generator producing 200 power. And two nodes who need 150 and 50
Now we would distribute the power through 1 and 3 line to the nodes 50 and 150 respectively.

Lets assume the line 3 breaks down. Then we can destribute 200 power on line 1, first node taking 50 and letting the other 150 flow through line 2 to other node.

Now this is a simple example, but if the graph is more complex and has various types of connections between nodes and generators.
How would one go about this problem? Is there a graph like method for assigning weights for edges (based on some conditions like maximum capacity and shortest path) like we have methods for finding shortest paths in graphs?

Should i even look at this as a graph problem or some other way?
Any help would be appriciated