I suspect this is what was causing some linear optimisation libraries (simplex style) to fail to find a solution when I had a problem with inputs in range 0.0-1

I suspect this is what was causing some linear optimisation libraries (simplex style) to fail to find a solution when I had a problem with inputs in range 0.0-1.0, but outputs expressed in hundreds of billions. If I scaled down my problem by dividing all the coefficients by one million, I am solving the same problem mathematically, but now those solvers are then stable and successful. I suspect they must be using some fixed epsilon to determine if the solved solution is close enough to the objective.