When investigating three network flow problems, a student finds:
a flow of 50 and a cut with capacity 50 ;
a flow of 35 and a cut with capacity 50 ;
a flow of 50 and a cut with capacity 35 .
In each case, write down what the student can deduce about the maximum flow.
The diagram below shows a network. The numbers on the arcs represent the minimum and maximum flow along each arc respectively.
By considering the flow at an appropriate vertex, explain why a flow is not possible through this network.
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(2 marks)