6. The table below shows the maximum flows possible within a system.
| To From | \(S\) | \(A\) | \(B\) | \(C\) | D | \(T\) |
| S | - | 35 | 30 | 55 | - | - |
| A | - | - | - | - | - | 50 |
| B | - | 12 | - | 8 | - | 20 |
| C | - | - | - | - | 15 | 30 |
| D | - | - | - | - | - | 14 |
| T | - | - | - | - | - | - |
For example, the maximum flow from \(B\) to \(A\) is 12 units.
- Draw a digraph to represent this information.
- Give the capacity of the cut \(\{ S , A , B , C \} \mid \{ D , T \}\).
- Find the minimum cut, stating its capacity, and expressing it in the form \(\{ \quad \} \mid \{ \quad \}\).
- Use the labelling procedure to find the maximum flow from \(S\) to \(T\). You should list each flow-augmenting route you find together with its flow.
- Explain how you know that you have found the maximum possible flow.
- Give an example of a practical situation that could be modelled by the original table.