Good question. I suppose by "manually" you meant by hand calculations possibly assisted by a desktop calculator? If so, in very simple cases, like 1 or 2 variables with 1 to 2 constraints, you could possibly use graphical methods to deduce them quite readily. Unfortunately, such solutions are also often trivial and uninteresting. For larger number of variables and more constraints, it would become very tough to do by hand, so much so that it would just be easier to use ready software (eg Excel solver) and "manually" set up Excel solver to generate the sensitivity report.

Thanks for the suggestion. I've been looking around for a more organized way of doing it. For now, have to seek you understanding to screen shot the slides.