title: How to solve a system of inequalities?
body: <p>I've reduced my problem (table layout algorithm) to the following problem:</p>
  
  <p>Imagine I have N variables X<sub>1</sub>, X<sub>2</sub>, ..., X<sub>N</sub>. I also have some (undetermined) number of inequalities, like:</p>
  
  <p>X<sub>1</sub> >= 2<br>
  x<sub>2</sub> + X<sub>3</sub> >= 13<br>
  etc.</p>
  
  <p>Each inequalities is a sum of one or more variables, and it is always compared to a constant by using the >= operator. I cannot say in advance how many inequalities I will have each time, but all the variables have to be non-negative, so that's already one for each variable.</p>
  
  <p>How to solve this system in such a way, that the values of the variables are as small as possible?</p>
  
  <p><strong>Added:</strong> Read the wikipedia article and realized that I forgot to mention that the variables have to be integers. Guess this makes it NP-hard, huh?</p>