Optimizing Traffic Flow with Linear Algebra

[morsel]

Homework Statement

Problem 42 in this pdf file: http://math.rwinters.com/E21b/homework/HW1.pdf

Homework Equations

The Attempt at a Solution

Starting from the section at the very bottom and going clockwise, let the sections be a, b, c, and d, respectively.

b + 300 = c + 400
c + d + 100 = 250
120 + 150 = a + d
a + 300 = b + 320

Solving these equations using elimination, I get:
a = 270 - t
b = 250 - t
c = 150 - t
d = t

How can I figure out the maximum and minimum traffic volume for each location?

 

[Dick]

The traffic flow numbers have to be nonnegative, right? Figure out the range of t that satisfies that restriction.