 #1
 64
 0
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+x6x5=55
x5x4=35
x6+x3x4=60
x3x2=40
x1x2=70
Reduced rowechelon 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+st
x2=15+st
x3=25+st
x4=35s
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+st=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?
Attachments

29.3 KB Views: 353