# Traffic Flow Pattern

## Homework Statement

1. What is the system of equations that describes the traffic flow?
2. The section of East Street between First and Second is under construction. Assuming that as few cars as possible use this block, what are the possible ranges of traffic flow on each of the other blocks?
(Hint: It is easiest if you order your variables in such a way that s becomes a free variable.)

http://img87.imageshack.us/img87/1944/linear.jpg [Broken]

## Homework Equations

Kirchoff Law: Flow going in equals to the flow going out.

## The Attempt at a Solution

We solved number one using MatLab

If A =

1 0 0 0 -1 0 0 100
-1 1 0 0 0 1 0 50
0 -1 0 0 0 0 -1 -350
0 0 -1 0 1 0 0 50
0 0 1 -1 0 -1 0 -300
0 0 0 1 0 0 1 450

rref(A) =

1 0 0 0 0 -1 1 300
0 1 0 0 0 0 1 350
0 0 1 0 0 -1 1 150
0 0 0 1 0 0 1 450
0 0 0 0 1 -1 1 200
0 0 0 0 0 0 0 0

Thus the equations are:

s = y - z + 30
t = 350 - z
u = y - z + 150
v = -z + 450
x = y - z + 200

For number 2 we are thinking that this deals with minimization(from Calc 1) however we are unable to come up with a relation that has only two variables.

For example,
u - x = -50
u = y - z + 150