Search

1 of 8 0-day streak

Determine and certify maximum flow

Question 1 of 8

Calculator allowed

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

Directed capacity network. Source P; sink T. Full edge list: P→C capacity 20 kg/min; C→T capacity 50 kg/min; P→E capacity 60 kg/min; E→M capacity 80 kg/min; M→A capacity 80 kg/min; A→T capacity 100 kg/min.2050608080100PTCEMA

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

Partially specified feasible-flow certificate. A question mark is an unknown, not zero
Directed edgeCapacityAssigned flow
P→C20?
C→T5020
P→E60?
E→M8060
M→A8060
A→T10060
(a)2 marks

Use capacity bounds and conservation to complete these certificate entries

(b)1 mark

Find and certify the maximum-flow value for the network