Shortest Path — practice questions

Networks · Part 3 of 5

3 exam-style questions with model answers, plus 4 quick multi-choice questions — every question on this part of the standard, grouped by the 1 page of notes they come from.

Write a full answer before you reveal the model one. That comparison is where the learning happens.

The shortest path

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AchievedShow

Find the shortest path from P to T in a network with arcs $PQ = 5$ , $PR = 2$ , $QR = 1$ , $QS = 6$ , $RS = 8$ , $ST = 3$ , $RT = 12$ . State the route and its length.

MeritShow

A courier drives from the depot D to customer Z. Travel times in minutes are $DW = 12$ , $DX = 9$ , $WX = 5$ , $WY = 14$ , $XY = 7$ , $XZ = 15$ , $YZ = 6$ . Because of a one-way system the leg $XZ$ can only be driven from X to Z. Find the fastest route to Z, and advise the courier on the return trip.

ExcellenceShow

In the pump-station network ( $AB=4$ , $AC=6$ , $BC=3$ , $BD=8$ , $CD=5$ , $CE=11$ , $DE=4$ , $DF=9$ , $EF=3$ ) the shortest route from A to F is 18 km. Roadworks will slow one arc. Determine which single arc, if any, could be lengthened without changing the shortest distance, and by how much each arc on the route could be lengthened before the best route changes.

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Covers AS91260