A linear program can be stated in the form:
subject to
where is in , is in , and is in
For a first example we have a simplex two dimensional linear programming problem of the form described above with:
The LPSolve command returns the optimal function values, as well as the point at which the optimal value occurs.
Alternatively, we could use the first two constraints and the nonnegative option.
The first element of the solution is the minimum value that the objective function obtains while satisfying the constraints. The second element indicates a point where the minimum is reached. This point is not necessarily unique.