Maths Quest Maths A Year 12 for Queensland
WorkSHEET 7.2
Chapter 7 Networks WorkSHEET 7.2
Networks
1
Name: ___________________________
/50
1
Consider the network flow diagram below
representing the flow of water between a
reservoir (A) and a town (H). The other nodes
(B…G) represent pumping stations.
Node B: Inflow =130, Outflow = 50 + 70 = 120
Node C: Inflow = 70, Outflow = 70
Node D: Inflow = 50, Outflow = 40
Node E: Inflow = 50, Outflow = 50
Node F: Inflow = 30 + 40 = 70, Outflow = 70
Node G: Inflow = 60 + 70 = 130, Outflow =130
Determine the inflow and outflow for each
pumping station.
6
Maths Quest Maths A Year 12 for Queensland
2
Chapter 7 Networks WorkSHEET 7.2
Convert the following flow table into a network Step 1: Create outflows from Node A.
diagram.
From
To
Flow capacity
A
A
B
C
1000
600
A
D
800
B
E
1100
C
C
E
F
400
100
D
F
600
E
F
1600
Step 2: Create flows from B and C to E.
By comparing the outflow at A to the inflow at
F, what is the maximum possible flow through
the network?
Step 3: Complete with flows from C, D and E
to F.
By examining outflow at A (1000 + 600 + 800)
and inflow at F (100 + 600 + 1600), the
maximum possible flow could be 2300.
2
6
Maths Quest Maths A Year 12 for Queensland
3
Chapter 7 Networks WorkSHEET 7.2
Modify the inflows and/or outflows at various
nodes so that the maximum possible flow
through the network is the same as the flow
out of Node A.
3
Maximum possible outflow = 2400
However, 200 is ‘lost’ at D, and 100 is ‘lost’ at
C yielding a flow of 2100 (question 2).
One possible modification is…
State the new actual flows through each node.
From
To
Actual flow
A
A
B
C
1000
600
A
D
800
B
E
1000
C
C
E
F
400
200
D
F
800
E
F
1400
5
Maths Quest Maths A Year 12 for Queensland
4
Chapter 7 Networks WorkSHEET 7.2
In deciding what roads to build, the traffic
capacity of a road needs to be considered.
Step 1: Add flows from A to B and C, B to D
and C to D.
4
6
A dirt road has a capacity of 0–20 cars per
minute, a single lane highway has a capacity of
30–40 cars per minute, and a dual lane freeway
has a capacity of 50–60 cars per minute.
Consider the traffic capacity of the following
network of roads connecting seven towns.
From
To
A
B
Traffic
capacity
40
A
B
C
D
50
10
B
C
E
D
20
20
C
F
F
D
40
20
D
E
G
G
60
20
F
G
30
Step 2: Add flows from B to E, C to F, F to D.
Step 3: Add flows from D, E and F into G.
Convert the traffic capacity table into a network
diagram.
5
The graph represents a road network joining
several towns. Find the shortest circuit that
travels through each town only once.
B–C–D–E–F–A–B
Shortest circuit  5  6  7  8  10  9
 45 km
6
Maths Quest Maths A Year 12 for Queensland
Chapter 7 Networks WorkSHEET 7.2
5
The next three questions refer to the following
network. Distances are in kilometres.
6
The roads are to be resurfaced between each
town in the network. Name one possible route,
starting at A, if all roads are to be travelled
once only.
A–B–C–H–E–D–H–B–E–G–A–F
–G–B–A
4
7
The local council is sponsoring a bike ride.
The cyclists are to pass through each town.
What is the minimum distance to be covered if
the event is to begin and end at town C?
C–H–D–E–G–F–A–B–C
11  12  20  16  15  23  18  19
 134 km
5
8
A telecommunications cable is to be installed
linking all the towns. Determine the minimum
length of cable required if it is laid beside
existing roads.
6
9  15  11  14  13  11  12  85 km
The next two questions refer to the following
graph.
Maths Quest Maths A Year 12 for Queensland
Chapter 7 Networks WorkSHEET 7.2
6
9
The length of the minimum spanning tree is:
A 43
B 45
C 55
D 58
E 61
B
3
10
The shortest path between A and D is:
A 24
B 25
C 26
D 27
E 28
B
3