Week 6 practice problems

Example

Consider the following network:

1. Find all shortest paths from $S$ to $T$ and determine the length $s$ of these.
2. Find all longest paths from $S$ to $T$ and determine the length $l$ of these.
3. For which arcs (if any) is it true that shortening that arc by one unit, leaving all others unaltered, will decrease $s$?
4. For which arcs (if any) is it true that shortening that arc by one unit, leaving all others unaltered, will decrease $l$?
5. For which arcs (if any) is it true that lengthening that arc by one unit, leaving all others unaltered, will increase $s$?
6. For which arcs (if any) is it true that lengthening that arc by one unit, leaving all others unaltered, will increase $l$?