The accompanying figure shows a network of one-way streets with traffic flowing in the directions indicated. The flow rates along the streets are measured as the average number of vehicles per hour. 375 800 350 200 800 200 250 225 (a) Set up a linear system whose solution provides the unknown flow rates. X2 = 25 X3- X4 = -600 X1 - X2 = 550 -X1 + X4 = 25 X2 - X3 = 550 X3 X4 = -600 - X2 = 25 -X1 + X4 = 25 X2 = 25 X2 + X3 = -600 X3 + X4 = 550 -X2 + X4 = 25 X2 = 25 X2 + X3 = -600 X3 + X4 = 550 -X2 + X4 = 25 (b) Solve the system for the unknown flow rates. X1= + S, X2 = +S, X3 +S, X4=S (c) If the flow along the road from A to B must be reduced for construction, what is the minimum flow that is required to keep traffic flowing on all roads? The minimum required flow 1 vehicles per hour.
The accompanying figure shows a network of one-way streets with traffic flowing in the directions indicated. The flow rates along the streets are measured as the average number of vehicles per hour. 375 800 350 200 800 200 250 225 (a) Set up a linear system whose solution provides the unknown flow rates. X2 = 25 X3- X4 = -600 X1 - X2 = 550 -X1 + X4 = 25 X2 - X3 = 550 X3 X4 = -600 - X2 = 25 -X1 + X4 = 25 X2 = 25 X2 + X3 = -600 X3 + X4 = 550 -X2 + X4 = 25 X2 = 25 X2 + X3 = -600 X3 + X4 = 550 -X2 + X4 = 25 (b) Solve the system for the unknown flow rates. X1= + S, X2 = +S, X3 +S, X4=S (c) If the flow along the road from A to B must be reduced for construction, what is the minimum flow that is required to keep traffic flowing on all roads? The minimum required flow 1 vehicles per hour.
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:The accompanying figure shows a network of one-way streets with traffic flowing in the directions indicated. The flow rates along the
streets are measured as the average number of vehicles per hour.
375
800
350
200
800
200
2501
225
(a) Set up a linear system whose solution provides the unknown flow rates.
X2
= 25
X3- X4 = -600
X1 - X2
= 550
-X1
+ X4 = 25
X2 - X3
= 550
X3
X4
= -600
X1 - X2
= 25
+ X4 = 25
X2
= 25
X2 + X3
= -600
X3 + X4 =
550
-X2
+ X4 =
25
X2
= 25
X2 + X3
= -600
X3 + X4 = 550
-X2
+ X4 = 25
(b) Solve the system for the unknown flow rates.
X1=
+ S, X2 =
+S, X3
+S, X4 =S
(c) If the flow along the road fromA to Bmust be reduced for construction, what is the minimum flow that is required to keep
traffic flowing on all roads?
The minimum required flow i
vehicles per hour.
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