Any number of the variables may be specified to be of type integer. This program solves problems of this kind. The result specifies values for all variables. Uses a 'Simplex' algorithm and sparse matrix methods, for pure LP problems. If one or more of the variables is declared integer, the Simplex algorithm is iterated with a branch and bound algorithm, until the desired optimal solution is found.
Maximization is the default.
So, the simplest linear problem consists of an objective function and 1 constraint. No real-life examples should be of this form, so I am not really chasing this problem. It is up to the user to interpret the result of this transformation. 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 not very good for numerical stability.