Linear programming with unknown constants

Greetings,

I have a function, which I want to minimize that looks something like this:

f=alpha*(x(1)+x(2)+...)

And constraints of the type:

x(1)*beta+x(2)*gamma+... <= 0

The alpha, beta, gamma, ... are unknown constants. I would like to solve my system with solutions that depend on these constants. How can I do that?

[John D'Errico]

You cannot solve this using linear programming, since changing those constants will completely change the solution. If the problem is bounded, any answer at all is possible, as long as it lies on the constraint boundary, depending on the values of those unknown constants.

At best, you could delineate a set in the constant parameter space that will yield a solution at each intersection of the constraints. For this, you will need to do some reading about linear programming.

[Hans Wurst]

I can solve these types of problems by hand with linear programming and I will get a solution that depends on the constants. This is exactly what I want Matlab to do.