The first thing to know is that feed comes from your dairy feed tank.
You can view your farm feed from the Management terminal or by logging in and viewing your feed audit on the farm details page.
Feed tanks are where milker stalls pull the feed from.
Feed Dispensers, like the fridge, are filled from your feed tanks but are then no longer connected to the feed tanks. This means that feed in a dispenser can not be retrieved by a milker. This feed is meant to be used by bulls mostly. Cows can also use this to feed when farm hands are not around.
Feed does give livestock a milking boost but the primary reason is to increase their daily limit. Higher level livestock benefit the most from feed as their rates are alot quicker and feeding can help them produce even more milk for longer.
Cows under level 12 don't benefit that much from feeding. One or two feeds a day to keep them from becoming punished for not feeding (from the muffinOs hud) is all that is needed.
Once these cows get over level 12, you start to see a good amount of bonus from maxing their feeding per day if they can maintaining milking till reaching their limit rate.
When you need more feed, dairy owners or manager farm hands can purchase feed from the Moolah store on the web. Once you purchase feed you must apply it from the dairy inventory.
To get Moolah for feed, most dairies rely on donations from livestock, farmhands, milk delivery, or completing achievements.