There are a few situations where lp_solve is known to give wrong "No
solutions".

- The problem consists entirely of constraints on just single variables
  (socalled "bounds", like x < 1; ) and no constraint with more than 1
  variable (like x + 3 y > 17; ). This leaves lp_solve with an empty problem
  matrix, as bounds are not stored in the main matrix. No real-life examples
  should be of this form, so I am not really chasing this problem.

- There are variables in the objective function which do not occur in a
  constraint with more than 1 variable, but just in a bound. This is a bug in
  lp_solve which I would like to repair, but I have sofar been unsuccesful.
  Anyway, this can easily be avoided, as the value of a variable just occuring
  in a bound and the objective function is trivially clear from the beginning.
  You can also just constrain the value of the entire objective function in the
  first constraint by a number which you know will not constrict your LP
  problem.

- Many people forget that lp_solve can only handle POSITIVE values for the
  variables.

- Sometimes problems are numerically unstable, and the unavoidable rounding
  errors inside lp_solve will cause wrong results. It is very hard to give
  general solutions to this problem, but try to keep all values in your problem
  in the order of magnitude of 1 by proper scaling. Almost parallel
  constraints are also note very good for numerical stability. Use
  "lp_solve -v" and observe the values of the pivots to see if there are any
  dangerously large or low numbers there.
