title: linprog gives wrong solution?
body: <p>I am trying to solve a linear programming problem in matlab, the input is </p>
  
  <pre><code>[weights,~,flag]=linprog(f,[],[],C,b,0,10);
  </code></pre>
  
  <p>so, according to the manual this should solve the problem <code>min f*x with the constraints C*x=b and 0&lt;=x&lt;=10</code>. So all entries of <code>x</code> should be positive. However the solution I get contains negative entries (see example to reproduce the issue below). The flag i get back is 1, which according to the docs means the method has converged. </p>
  
  <p>What am I doing wrong?</p>
  
  <p>here is the input </p>
  
  <pre><code>C =
  
      19    20    18    20    18
       3     3     4     5     3
       1     1     1     1     2
       1     1     1     1     1
  </code></pre>
  
  <p>and </p>
  
  <pre><code>b =
  
      19
       4
       1
       1
  </code></pre>
  
  <p>and </p>
  
  <pre><code>f =
  
       1
       1
       1
       1
  </code></pre>
  
  <p>the result is </p>
  
  <pre><code>weights =
  
     84.1104
    -62.8328
    -41.5552
     21.2776
     -0.0000
  </code></pre>