This /r/theydidthemath Reddit thread asks how much weight each bracket holds in the photo below.
During graduate school I spent long periods of time waiting on data acquisition and goofing off in the lab. The following video is the ~hour long process of simulating this scenario using Solidworks, in a display of incredibly unnecessary technical work. This could be reduced to a relatively simply force-body diagram by a clever person (who wasn't looking for excuses to procrastinate).
It was clear that some posters were making faulty assumptions to simplify the problem. The cross-sectional area of a bottle is not linear along its height, so it's not a linear mass relationship along the shelf. The group of bottles also have a different center of mass than the group of liquid.
My assumptions: bottle wall thickness, material densities of the liquid, glass, and shelf, and support width. Most importantly, I assumed that the bottles only act on the shelf-- they aren't sliding down and acting on one another. In essence, I'm assuming the strength of static friction between the bottles and shelf is high enough to hold them in place at this angle.
Conclusions: The left support holds ~40% and the right support holds ~60%. In my simulation I'm finding 11.98N and 17.8N reaction forces for the two supports.