Cyb: Of course, there were lots of people in precolumbian America who farmed. I'm fully aware of that.
Brandrinn: That's a good calculation, but I'm not quite sure.
When your example guy collects one man-day worth of food (let's call it a "unit" for simplicity) to bring to the city, he has an average output of 1/5 unit/day delivered. But that's assuming he only delivers one unit each time, which would be very inefficient. Assuming that he collects six units in a day, he could just forage for one more day before leaving, bringing his output up to 1 unit/day.
The question is, how much can a guy carry? According to Planet Construction Kit, a marching soldier can carry about 70 pounds, and needs 3 pounds of food in a day. So he should easily manage 20 units.
Then we have to take into account that there's not an unlimited amount of food two days away either. Which is when this little exercise starts getting really messy. But let's simplify.
We look at an area five days' walk from the city. A carrier who doesn't do the foraging himself would have a minimum output of 1 unit/day. Someone needs to do the foraging - let's say you can forage 5 units/day. The radius is 10 times what you said, so the area is 100 times bigger, so the maximum population of that whole area is about 20 000. Result: 4000 foragers, 8000 carriers, 8000 city dwellers. That's basically under the assumption that all the food is five days away, so it's a low estimate.
(A more precise calculation should be a pretty neat exercise in calculus. But I'm just not in the mood.
Then there are other modes of transport. If there are some kind of roads, it should be possible to move things a little bit more effectively. Why not invent the wheel? And of course, boats.
On an even less realistic note - you know what would be awesome? Unmanned boats! Suppose there is a river with a lot of little branches. The people place rocks or logs along each stream to make sure the edges of the stream are smooth, and then they have boats that are round, so they don't get caught on anything. The boats could even have like a roof, so they don't risk flipping over... okay, they could basically be barrels. Then the people would send the barrels/boats down the stream, and they would float along merrily all the way to the capital at the mouth of the river.
How come people don't do this? Maybe I'm just too tired to see why it's a stupid idea. Yep, probably time for bed.