I can just give general guidelines based on the formulas.
A complete analysis is pretty tedious but the International Residential Code has tables if you use conventional lumber.
Bolting lumber together makes the analysis more difficult.
The LVL people will recommend the correct product for your application, but they of course will be biased into selling you slightly more strength than you need. For whatever they recommend, ask what safety factor is built into their calculations.
A structural/civil/mechanical engineer can give you a size, either by hand or by using expert system software.
A college student or professor may advise you for free, like in this movie
http://en.wikipedia.org/wiki/Erin_Brockovich_(film)
People are happy to talk about their work, even if you don't look like Julia Roberts.
And, cantilevered beams are very complex to size.
It's one thing if only your life depends on your doing this correctly, but there are more lives at stake here.
For this same reason I refused to provide a stock car driver with a circuit that would prevent wheelies. BTW, vehicle dynamics are way more complex than beam sizing, not even taking into account driver reactions.
Thank you for asking. Way too many OPs are not as curious as they should be.