Help me buy groceries on $10-15?!
Store brand beans and rice. You're probably better off buying a loaf of bread for a dollar than buying a package of yeast, honestly. If it were longer than a week, I'd say otherwise. You can also buy some cheap spaghetti and make sauce out of just butter (cook is on medium on a stove until it tinges brown). YUM!
Don't get cheese, it's expensive. Eggs are a good idea.
If you are very low income you can apply for food stamps. I didn't think I could get them but I did, and it didn't take very long. The cheapest food you can buy is eggs, rice, pasta, and potatoes. Some lean ground beef, some shredded cheese or parmesan cheese, tomato or spaghetti sauce, and some canned or fresh vegetables would be things you could use with them. Peanut butter is something you can get for $2.00 and make sandwiches with. And ramen soup has kept me from starving before.
Go dumpster diving. It sounds pretty unappealing but most of the food grocery stores throw out is actually good and just has some packaging defects (stay clear of the meat and dairy if you do it though).
Buy some potatoes, rice, pasta, maybe some oats or kasha to make cereal, pick up a bag or two of frozen veggies, beans/lentils are a great cheap way to get tons of protein, if you don't want to buy expensive yeast and have baking powder it can be used as a leavening agent in making breads.
I feel like these are relatively cheap. Fruits, vegetables are still very cheap good
Potatoes, rice and pasta to start with.
Fresh or frozen veges.
Meat fish and chicken
Work out what you can get with the money you have.
Remember that the potatoes, pasta and rice will span over a couple of weeks.
Buy 14 double cheeseburgers from Mcdonalds.
Dried beans/legumes are super cheap. You could make lentils or split pea soup for about $5 and eat for a week.
bag of potatoes
and make cornbread