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## Homework Statement

I am doing an assignment in my Linear Algebra class. But I don't know how I will go about solving this problem.

So the problem is a network of water pipes. I start with a matrix and I get the solution to the system from the RREF matrix. All the flow directions are set, so the variables(x1,x2,x3,x4,x5,x6) cannot be negative because I cannot have "negative flow".

The problem text says that since all the x-variables have to be non negative I should get 6 inequalities (x1 bigger than or equal to 0) and (x6 bigger than or equal to 0)

but I don't see how?

I also have to minimize flow between two nodes, how do you go forward doing that?

What method gets me from matrix system of equations to inequalities?

Nothing about this in my book and I have spent countless of hours on the net, and still I can't figure this out.

## Homework Equations

The RREF matrix:

1 0 0 0 -1 -1 -20

0 1 0 0 1 1 50

0 0 1 0 0 1 40

0 0 0 1 1 0 10

0 0 0 0 0 0 0

## The Attempt at a Solution

I get:

x1= -20 + x5 + x6

x2 = 50 - x5 -x6

x3 = 40 - x6

x4 = 10 - x5

x5 = free variable

x6 = free variable

No inequalities here..