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## Linear programming piecewise linear objective [closed]

Ok, the problem was solved by a colleague with a bit more math education than me. It turns out the solution was not very difficult, hinging on a better understanding of what duals are. Still i don't understand why, given the supposed audience here and the apparent simplicity of the solution, no-one could propose an helpful solution in 24 hours time.

Hi list,

I'm trying to express this linear program as a minimization problem and i couldn't do it.

$\max x_1$

$x_1 <= \delta$

$x_1 <= 0$

Where $\delta$ is some (not necessarily positive) constant.

Would anyone please be kind enough to help me out,

Best

Ok, i'll adress the new comments below:

Is the aim of the of this forum to be helpful or pedantic ?

Ok, i'll address the comments i got so fare below:

Shake Baby & Yemon Choi:> This is not an homework, but an actual problem i'm trying to solve. Yemon Choi:> I'm not sure how much interest to a mathematician this problem will be, but i have tried several approach and none of them could do it, for example:

$\min x_1+\epsilon^++\epsilon^-$

$x_1>=\delta$

$x_1>=0$

$\epsilon^+>=0$

$\epsilon^->=0$

$\epsilon^+ +\epsilon^-=\delta$

I think I'm missing something and hope that someone accustomed to linear programing can help.

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It is also not clear to me where the difficulty lies with your question, unless there's a typo. What do your two constraints actually mean in your understanding? – Yemon Choi Apr 25 2010 at 22:47
And thirdly: forgive me if this sounds brusque, but you did look at the FAQ for this site, right? – Yemon Choi Apr 25 2010 at 22:47
This should be closed as HW. – Shake Baby Apr 25 2010 at 23:08
If you want to express max as a min, you need to switch to the dual problem. That is the very first thing one learns in linear programming. I'm voting to close. – fedja Apr 26 2010 at 2:33
I was also going to vote to close. It could be that there's some big gap in my education, but I can't make much sense of the question. My guess is that you're trying to maximize $x_1$ subject to the condition that $x_1$ is less than $\delta$ and less than $0$, but some English explaining what you're actually trying to do would really help. As is, it seems like you're just trying to compute $\min\{0,\delta\}$. – Anton Geraschenko Apr 26 2010 at 18:59
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