Eltalia, here right now there is not enough nectar coming in to sustain 4 frames of bees with 2 frames of
brood, much less expand that hive.
As a statistic (historical fact) for your localised area, fine. All local to you
would have to accept this given your experience level.
Yet the original post does not mention brood, pretty safe to assume
that area was not examined, given tbe post reads as a lid lift and
peek in.
My suggestion is brood being present would be a problem.
A queen doesn't need to be caged since she will only lay what eggs the bees can cover.
And when there is sugar and patties thrown in there the bees will max
that ability out, mistakenly.
Next, we have about a 2 month honey flow, 2 month mini flow, and 8 months dearth.
Most beeks feed in early year to have a foraging force during that 2 months. Queen
breeders and package suppliers start feeding sugar and pollen sub in late December.
Natural, non-fed bees will be lucky to give 15 KG. excess honey for the beek each year.
We are not in a great honey area. Alabama is a bit better, but still not a great producing area.
Sooo.. in a nutshell your local is endeavouring to create a honey producing
activity in an area not suitable for such an enterprise.
Using the word "natural" does not place the blame for performance - lack of in your
judgement - on the bees... is what I get from that read.
Bill