$1.50 per person or for all three? I too can eat reasonably on $1.50 for myself, by, as you say, cooking. Oatmeal, soups, stews, etc. In fact I often do, though because I like my home-made soups, not because I have to (anymore.)
1.50 a person. Heck, get a big bag of potatoes. Cook that. Mash them You’ll be full on a couple of potatoes and spend about 30 cents.
I guess $100/mo figures out to about 3.33/day for 4 people. The key is to build upon the previous days meal, like Pot Roast to beef stew to vegetable soup, etc. But it can be done. The local country bulk store has great deals on flour, oatmeal, corn meal, etc. (Bread on Tuesday is 50cents a loaf)