My area is much like Jacks.
Knowing the limit is a real pain, because the limit is different every year. Last year it stopped raining about mid June,and we did not get any substantial rain (more than a tenth) until September. It was a rough summer with quite a bit of feeding. They had plenty of pollen but very little nectar. This year we have had an abundance of rain. I have 26 hives in my home yard and they are ALL packing in the nectar. I think I could probably have 35 to 40 hives here this year and be fine.
I have three ponds within a couple hundred yards, and a creek about a 1/4 mile away. MOST of the land is tilled, but there are also pastures, draws, fence rows and crick bottom within very easy forage range. To the east is a large tract of timber (500+ acres) with locust, maple and many other hardwoods. As long as we get the rain we need, I think I could manage about 30 hives per yard.
I have also read somewhere in the past, that competition widens the area bees will forage. With one or two hives they typically forage within a mile, but as the competition grows they automatically extend that range. Obviously I cant confirm that, but I will say I have been quite happy with the amount of honey being produced, despite having more hives than I like in one spot.