sci.op-research

humberto.bortolossi@gmail.com wrote:
> Greetings!
>
> Is there a mathematical software that solves symbolically a parametric
> linear program, like that one:
>
> min x + y
> subject to ax + y >= 4
> bx + y >= 7
> x >= 0, y >=0
>
> That is, I would like to see the solution in terms of the coefficients
> a and b:
>
> (x*, y*) = (3/(a - b), (4a - 7b)/(a - b)) if 7/a <= 4/b
> (x*, y*) = (7/a, 0), otherwise.
>
> Thanks in advance, Humberto.

I don't think so. For a small example such as yours, you might get some
traction using a computer algebra package (Mathematica, Maple, ...) and
breaking the problem into cases. To use your example above, two of the
four inequality constraints must be binding at the optimal solution.
Hypothetically, you could solve all six combinations symbolically and
get six candidate solutions. Not all would be feasible, and among the
feasible ones not all would be optimal, but you might be able to derive
conditions on a and b such that if (a, b) satisfies ___ then ____ is the
optimal solution. Obviously, this approach would be useless for
anything larger than trivial problems.

/Paul