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13.02 Shortest paths

Worksheet
Edge weights
1

Consider the following networks:

a
i

State the weight of the edge from S to Q.

ii

Calculate the weight of the entire network.

b
i

State the weight of the edge connecting Q and S.

ii

Calculate the weight of the entire network.

2

Calculate the weight of the following paths in this network:

a

Path Y-E-D

b

Path A-B-Z-X

c

Path X-C-A-B-Z

3

Find the weight of the following subnetworks, highlighted in green:

a
b
4

Calculate the weight of the following paths in this network:

a

Path from Y to X

b

Path from Z to C

c

Path from B to X

Shortest paths
5

A group is organizing a tour for the elderly in a park, ending with a picnic. The given graph displays the map of the park:

Calculate the path which gives the shortest distance from the start of the park at vertex A, to the picnic area at vertex J.

6

The given map shows all possible routes in Mohamad's town. Mohamad travels from his home to his friend's house on a daily basis.

If Mohamad's house is vertex C, and his friend's house is vertex I, determine the shortest path between the two houses.

7

A grocery store is known for its fast deliveries across the town as shown in the following map:

If the store is at vertex A, and a delivery has to be made to vertex H, determine the shortest path the driver should take.

8

The police department receives a call about a robbery in progress at a grocery store. The given graph shows the map of the town:

If the nearest police car is located at vertex D and the grocery store is at vertex I, determine the shortest route the police should take.

9

A firefighting department received an emergency call about a house fire across the town represented in the following graph:

If the firefighting department is located at vertex L, and the house is at vertex A, determine the shortest route the firemen should take.

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Outcomes

ACMEM084

optimise distances through trial-and-error and systematic methods; for example, shortest path, routes to visit all towns, and routes to use all roads

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