Determine and certify maximum flow
A directed network represents a component-handling network. The source is S and the sink is K. Each edge label is its capacity in items/h. The network transfers components each hour; intermediate vertices pass on all incoming flow
Use inspection to allocate a feasible flow before checking its upper bound
The table specifies one particular feasible-flow certificate, not every possible feasible flow. Keep each displayed flow fixed and determine only the question-mark entries using conservation. Flow and capacity use the same units shown above. The diagram labels are capacities, not assigned flows
| Directed edge | Capacity | Assigned flow |
|---|---|---|
| S→A | 20 | 20 |
| A→K | 40 | 20 |
| S→C | 70 | ? |
| C→K | 110 | 70 |
| S→F1 | 20 | ? |
| F1→C1 | 40 | 20 |
| C1→A1 | 60 | 20 |
| A1→K | 40 | 20 |