Determine and certify maximum flow
A directed network represents a grain-transfer network. The source is P and the sink is T. Each edge label is its capacity in kg/min. The network transfers grain each minute; 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 |
|---|---|---|
| P→C | 20 | ? |
| C→T | 50 | 20 |
| P→E | 60 | ? |
| E→M | 80 | 60 |
| M→A | 80 | 60 |
| A→T | 100 | 60 |