Problem 13.3 Consider the network of streets with intersections A, B, C and D below. The arrows indicate the direction of traffic flow along the one-way streets, and the numbers refer to the exact number of cars observed to enter or leave A B,C and D during one minute. Each x; denotes the unknown number of cars which passed along the indicated streets during the same period. X1 B X4 X5 4 -A C x2 X3 a) Write down the linear system which describes the the traffic flow, together with all the constraints on the variables xi, i 1,...,5. (Do not perform any operations on your equations: this is done for you in (b).) = b) The reduced row-echelon form of the augmented matrix from part (a) is [1 00-1 0 10] 01 0 1 1 |│ 1 0 0 1 1 1│ 4 0 0 0 0 0 0 | Give the general solution. (Ignore the constraints at this point.) c) If AC were closed due to roadwork, find all possible traffic flows, using your results from (b).

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