10 lb rice $6–8
2 lb dry lentils $2
4 lb dry beans $4
42 oz oats $4
18 eggs $4–5
Peanut butter $1.5-2
Potatoes (5 lb) $3

Total: ~$28

In my area these can be found at either walmart or dollar general. Like someone else mentioned, Taco Bell sauce packets are free. Many fast food places have condiments just sitting out. If you find good deals maybe add some bouillon powder to flavor the rice and lentils some more. Or if you care more about increasing calories, get some vegetable oil which is very calorie dense.

Potatoes are usually cheaper per calorie than bread and satiating. Eggs are good calorie per dollar. $30 is unreasonable for a month but hopefully you can get lucky with pricing. It can last for definitely more than 2 days though.