4 The network below represents a system of water pipes in a geothermal power station. The numbers on each arc represent the lower and upper capacity for each pipe in gallons per second.
\includegraphics[max width=\textwidth, alt={}, center]{5ff6e3bb-6392-49cf-b64d-23bc595cd92e-04_837_1413_493_312} The water is taken from a nearby river at node \(A\)
The water is then pumped through the system of pipes and passes through one of three treatment facilities at nodes \(H , I\) and \(J\) before returning to the river. 4

1. The senior management at the power station want all of the water to undergo a final quality control check at a new facility before it returns to the river. Using the language of networks, explain how the network above could be modified to include the new facility. 4
2. Find the value of the cut \(\{ A , B , C , D , E \} \{ F , G , H , I , J \}\) 4
3. Tim, a trainee engineer at the power station, correctly calculates the value of the cut \(\{ A , B , C , D , E , F \} \{ G , H , I , J \}\) to be 106 gallons per second. Tim then claims that the maximum flow through the network of pipes is 106 gallons per second. Comment on the validity of Tim's claim.