I'm trying to write a linear programming problem whose solution determines whether a certain vector b is or is not a convex combination of A_1....A_n and if so, expresses b as such a convex combination.

I know what the constraints should be and really I'm just stumped at how to fill in this blank...

Maximize z = _______________ such that
Ax = b (for all A and x vectors)
x1 + ... + xn = 1

Any help would be greatly appreciated! Thanks