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"vKirchhoff's first Law, the flow into an intersection is equal to the flow out. This gives the followingystem

The augmentedmatrix of the above system is

~

1 0

1 -1

0 10 0

0 0

0 0

0 0 1 0

0 1 0 0

-1 0 0 01 0 0 0

0 1 0 10 0 1 1

0 800

0 400

0 600-1 -1200

-1 0

0 1000

800 - x + v (A)u + x - y + 400 (B)

Y - z + 600 (C)1600 + z . t + 400 (D)

t - u + W (E)v + w - 1000 (F)

Therefore, the solution can be written as

x - w - 200

y- t -600z - t - 1200

" - t - w

" - 1000 - w

w) t elK

OM VIr"J Jt~ . (.J~;;!OO, -t?lo.oo, (iew) , W:((OOV

1000 '7 /.A.! ~.1oo IF,orinstance, ifw:300 and t=1300 (in vehicles per hour), then i ,,(aoo J

~-100, y-700, z =100, U= 1000, V -700. w,tE"d:

Supposenowthatthe streetstrom A to B and trom B to C must be closed(for constructionfor instance),that is x=Oandy=O.Howmightthe traffic be rerouted?

To answer this question, set x=y=O in the above solution, we get W - 200, t - 600.z =-600. U =400and

V =800. Of course, the negative value for zis not normal. In order to avoid negative flow, we mustreversedirectionsonthe streetsconnectingC and D; this changemakes z =600insteadof z =-600.

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