It would depend greatly on your climate and the quality of your land (soil fertility, availability of water et cetera).
My grandmother (born in the early 1920s) grew up on her family's 69 acre dairy/poultry farm in North Carolina. The family had 6 people total, although the oldest children were almost adults before the last child was born. Everything they ate came from the farm and they still had enough milk and chicken left over to sell. The farm must have been very profitable (and the whole family is full of tightwads). My grandmother's youngest sibling still has 39 of the original acres (the rest was divided when my great-grandfather died in 1952). When my great-grandmother died last year she left enough cash for her grandchildren to get some of it.
But, here in Florida we have poor soil and poorer soil. We also have every kind of bug, mildew, rot and mold imaginable. And any farm can easily grow a bumper crop of weeds. NC and Fl both get about the same amount of rain. But in NC you get a little rain about every 3 days. In Florida you may get no rain for 3 months and then have it rain every day for a month. With our soil, climate and growing conditions I doubt that anyone could grow enough food and enough variety of foods to be completely self-sufficient here.
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