Networks-Maximum total flow help!

[tcstudent]

asked my teacher, still cant understand it and i have a sac tomorrow and dont know this omg

the question is #6 The maximum total flow from node A to node G

[masonruc]

C

[tcstudent]

i really need to know the procedure of how to find that the answer was actually C?

[brenden]

The thing you want burned into your head is "minimum cut = maximum flow".
I'll explain. Picture you have heaps of cara driving from point A to point G. Each road can only have a certain amount of cars on it before traffic piles up. The instant traffic piles up, the flow of cars begins to slow. If you find the minimum cut, you've found the numbe of cars that can be on the roads before traffic starts to congest. In this case, 23, because that's the smallest number you can make from a 'cut' (or blocking off traffic with a giant line).
Once you have the cut, think of 24 people trying to go through the network. It's fine for the first two roads, but when we get to the cut, one car has to be left out, because 14 goes to 13.
Make sense?

[lala1911]

Wow networks and decision making is so tricky. Now I know how methods students feel when I tell them to just apply for formula.
What was said above is right, but how I like to think of it is:

10 cars go to road B, and from B to E theres 16 lanes, so the 10 can keep progressing, and from E to G, theres 11 lanes, so those 10 can keep progressing to the finish line.

14 cars go to road C, from C to D theres only 13 lanes, so one must drop off, from D to F theres 20 lanes, so the 13 can keep progressing, from F to G theres 22 lanes, so the 13 can eep progressing to the finish line.