My wife and I tried to do this recently on $1.70 per person per day. We didn't last our intended 28 days. A few observations we found:
Meat and organic food was too expensive.
Fruit is crazy expensive so we bought OJ from concentrate with no additives as a cheap source of Vitamin C.
Eggs were are very expensive, but we needed the protein and nutrients, so rationed ourselves to 3 each per week.
We had to remove all sugar to save on cost and sugar crashed badly.
We decided that Costco was cheating due to the $70 membership fee and so we alternated between Safeway and Walmart.
You quickly learn the difference between broccoli florets and stems. [Stems are cheaper]
Baking your own bread is incredibly cheap and if you're using a sourdough starter you just need flour, salt and water. It's a great staple and adds taste to the meal. I scraped the unused flour off the work bench and dumped it back in the sourdough starter to save on cost.
Lentils are the most complete non-meat protein source.
Combining beans and rice give you a complete protein.
Cheese is too expensive and you can't make cheese from regular organic off-the-shelf homogenized ultra-pasteurized milk. It just doesn't set when you add the rennet.
You can buy coffee for $1 for a months worth of ground coffee at walmart. It's called Master Chef and it tastes like a used catbox.
Before we did our experiment we found a few "living on a dollar a day" blogs, but every single one bought in bulk and then calculated the cost of each scoop they took out of the bin. They also didn't care about nutritional completeness and basically starved themselves for the period.
After trying to do this on $1.70 and failing, I think Mike's budget of $3 is probably a realistic per person budget if you're going to stay healthy.