Route X

$1.$ Start from Voyager

$2.$ From Voyager travel to Planet $20$

$3.$ From Planet $20$ travel to Planet $2$

$4.$ From Planet $2$ travel to Planet $13$

$5.$ From Planet $13$ travel to Planet $11$

$6.$ From Planet $11$ travel to Planet $3$

$7.$ From Planet $3$ travel to Earth $($Home$,$ Sweet Home!$)$

Network Diagram $2$ shows the possible routes through the Delta Quadrant, where the nodes are different worlds, planetary system and space anomalies, and the values on the branches are the actual distances, in light$-$years, between nodes. Question $1$: Using Network Diagram $1,$ determine the maximum flow from the Source to the Sink in the network.

$-$ Assume that all branches are directed, with flow capacities indicated for each branch. For example, flow from Source to B is $18$ units at most; and flow from B to Source is $0$ units at most.

$-$ If you are having trouble seeing the network or reading the numbers clearly, do not worry. An image version of the network diagram is available on Brightspace. Please refer to the Exam IV Module, Images submodule. This is Network Diagram $1.$

Using Network Diagram $1,$ the maximum flow through the network from Source to Sink is

units.