Think of all the ways peeps can get food, then remove all of the sources except the one you can control most rigidly. You need to store up a bunch of food beforehand to keep your good peeps fed, or grow veggies with an eye on the clock so you can harvest before the hungry peep can grab it. It takes several days and you need to be ready for heartwrenching pleas for food. (Sometimes they don't beg though.)