title: Linear program question
body: <p>I'm trying to prepare for my midterm and  I was going over some problems out of my algorithm book but can't seem to figure out the following problem:</p>
  
  <p>Find necessary and sufficient conditions on the reals a and b under which the linear program </p>
  
  <pre><code>max: x+y
  ax + by &lt;=1
  x, y =&gt;0
  </code></pre>
  
  <p>(a) is infeasible.
  (b) is unbounded.
  (c) has a finite and unique optimal solution.</p>
  
  <p>here is what I've come up with:
  for (a), we can add another constraint: ax+by=>5</p>
  
  <p>I'm not sure what to do about b and c.I'm not sure If I'm allowed to change the constraints I'm already given or add new ones.</p>
  
  <p>Any help will be appreciated.
  Thanks so much advance.</p>