Dharma, and later the others, farmed foods such as meat and fresh vegetables and fruit. The food drop for the Swan didn't seem to include any food that wasn't in boxes/tins/packets. Mikhail has cows outside and meat in the chiller inside the Flame. The Others would be able to survive for a long time, after the food drops stopped, on the farmed produce. The 815 survivors lived on boars and fruit for weeks before discovering the Swan station.
DHARMA most likely buys bulk food and repackages it in there own containers. its like with the army, you don't see soldiers eating brand name foods, they eat generic food. also, the D.I. isn't going to go and blow all its money on brand name foods, its not like people are going to complain, there stuck on an Island.
Dharma were unaware of the tunnels underneath the barracks, otherwise they would have explored then. Equally, the others wouldn't have stored Jughead there.