2
$\begingroup$

I have function $\max \{ |x-1| + 2|y-1| | x,y \in R, x+y \leq 2 \}$. Can this problem be converted to LP? I think it cant because of the abs. value in criterial function, but Im not sure.

If it can, how to convert it? I think that restrictive conditions are already in correct form so I only have to convert criterial function to some form without abs. if its possible.. Thanks for advice!

  • 0
    So you suggest dividing the equation into four different with corresponding restrictions? I dont know if its LP after that but maybe youre right...2012-12-05

1 Answers 1

2

Yes, it can be converted into LP. Use the following hint

Hint: $|z|$ can be replaced by $z^{+}+z^{-}$ along with the conditions $z^{+}\geq 0, z^{-}\geq 0$.

  • 0
    @Smajl: You replace $|z|$ by $z^++z^-$ in the criterial function as well.2012-12-06