Originally Posted by

**LutherBlissett** Hello everyone,

I am not really sure where to post about Linear Programming. I am trying to program an LP problem using PuLP, as I am very familiar with Python.

I faced the issue of having decision variables which can take negative value,

i.e. they are bound between -k1 and K2. I have seen the advice of introducing

a new variable into the problem, so the original cosntraint is shifted in

order for the new variable to be non-negative only. I'd guess that the

substitution has to be carried out throughout the problem, i.e anywhere the

original variable appears (including objective function) but I would be

grateful if someone could confirm this.

Below I have written a simple problem and the reformulated proble.

I would like to know:

- is what I am doing correct?

- is there a better approach to this problem?

Many Thanks in advance

Paolo

Original problem,

Max -p1x1 - p2x2

x1 >= -10

x1 <= 20

x2 >= -30

x2 <= 40

Inv + x1 >= 0

Inv + x1 + x2 >= 0

Inv + x1 <= TC

Inv + x1 + x2 <= TC

with TC and Inv being positive constants