1. The diagram below shows a network of one way and two way roads in Melbourne. The diagram shows the number of vehicles travelling on each section of road and the direction of the traffic flow during a typical 15 minute period on a weekend. Vehicles can only enter the network at points B and D, and leave the network at A and C. 85 X₂ 40 20 20 25 D X₁ 70 100 X₁ 30 60 (a) Derive (with detailed working) a system of linear equations that describes the traffic flow in the road network. (b) Reduce the augmented matrix for the system in part (a) to reduced row-echelon form. Indicate which row operations you have used. (c) Using part (b), determine the number of vehicles 1, 2, 3 and 4 in the road network. (d) Determine the minimum number of vehicles in the road joining B to C. Justify your answer.
1. The diagram below shows a network of one way and two way roads in Melbourne. The diagram shows the number of vehicles travelling on each section of road and the direction of the traffic flow during a typical 15 minute period on a weekend. Vehicles can only enter the network at points B and D, and leave the network at A and C. 85 X₂ 40 20 20 25 D X₁ 70 100 X₁ 30 60 (a) Derive (with detailed working) a system of linear equations that describes the traffic flow in the road network. (b) Reduce the augmented matrix for the system in part (a) to reduced row-echelon form. Indicate which row operations you have used. (c) Using part (b), determine the number of vehicles 1, 2, 3 and 4 in the road network. (d) Determine the minimum number of vehicles in the road joining B to C. Justify your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. The diagram below shows a network of one way and two way roads in Melbourne. The diagram
shows the number of vehicles travelling on each section of road and the direction of the traffic flow
during a typical 15 minute period on a weekend. Vehicles can only enter the network at points B
and D, and leave the network at A and C.
85
X₂
40
20
20
25
D
X₁
70
100
X₁
30
60
(a) Derive (with detailed working) a system of linear equations that describes the traffic flow in
the road network.
(b) Reduce the augmented matrix for the system in part (a) to reduced row-echelon form. Indicate
which row operations you have used.
(c) Using part (b), determine the number of vehicles 1, 2, 3 and 4 in the road network.
(d) Determine the minimum number of vehicles in the road joining B to C. Justify your answer.
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