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## Homework Statement

Consider the network of streets with intersections a,b,c,d and e below. The arrows indicate the direction of traffic flow along the oneway streets, and the numbers refer to the exact number of cars observed to enter or leave a,b,c,d and e during one minute. Each xi denotes the unknown number of cars which passed along the indicated streets during the same period.

See Attached Image

Linear System:

x1+x6-x5=55

x5-x4=35

x6+x3-x4=60

x3-x2=40

x1-x2=70

Reduced row-echelon form

1 0 0 0 -1 1 | 55

0 1 0 0 -1 1 |-15

0 0 1 0 -1 1 |25

0 0 0 1 -1 0 |-35

0 0 0 0 0 0 |0

s t

General Solution:

x1=55+s-t

x2=-15+s-t

x3=25+s-t

x4=-35-s

x5=s

x6=t

The question is: if ED were closed due to roadwork, find the minimum flow along AC, using your results in the genral solution.

Note: x2 = ED therefor x2=0, and AC is x6

## Homework Equations

## The Attempt at a Solution

I know x2=0 and no idea what to do with S and T...

what I did is set x2=0 so -15+s-t=0 so S=t+15

And sub it into the general solution you get:

x1=70

x2=0

x3=40

x4=-20+t

x5=15+t

x6=t

so x4≥0 when t≥20

x6≥0 when t≥0

So minflow is 0?