title: Find positive solutions to underdetermined linear system of equations
body: <p>Consider a problem of the following:</p>
  <p>Find <code>x_1, x_2, x_3 &gt; 0</code> such that</p>
  <pre><code>67.5 = 60*x_1 +  90*x_2 + 120*x_3 and
  60   = 30*x_1 + 120*x_2 +  90*x_3
  </code></pre>
  <p>In this case I want the solution</p>
  <pre><code>0 &lt; x_3 &lt; 3/7,
  x_2 = 7/20 - 4/10*x_3, and
  x_1 = 2/5  -  7/5*x_3
  </code></pre>
  <p>Is there a easy way to make Matlab solve such a problem for me?</p>