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
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
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
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:
so x4≥0 when t≥20
x6≥0 when t≥0
So minflow is 0?