We live in the woods and have the occasional field mouse or wood rat show up. It used to be really bad but we keep the
Tomcat disposable rat and mice bait stations out all the time now. Haven't seen a mouse or rat, live or dead, near the house or barn in years now, but over time the bait still disappears.
If you have the number of rats you claim, it will take awhile to get rid of them. First thing to do is stop feeding them ... it takes a lot of, easy to get, food to sustain that many rodents. As mentioned by other posters, you need to rodent proof all of your feed storage containers and feeders. Once you start putting the bait stations out you must keep doing it. Even after you
THINK all the rodents are gone. Every few days make a round of the bait stations and check that they still have bait left. If they are empty, replace them immediately.
In the beginning you may be replacing bait stations daily, but as they eat the bait and die you will start seeing fewer and fewer rats/mice. You can confirm this by the longer times in between bait changes.
Some folks have mentioned single kill or live traps. If you have one or two pests these may help out .... if you have bunches of them you will never be able to control them by killing them one at a time.