Subsidised Farms and the Ministry of Agriculture increase Food production, while the Rations Warehouse is used to store Food not consumed by your troops. This food would otherwise be lost.
Rations warehouses are researched in the 1st era, Subsidised farms in the 2nd and Ministry of agriculture in the 3rd. So they aren't all available at the same time.
Also use empty slots in your military academies to store troops. Those troops will not consume food. Note that troops who are not in your own territory (i.e. when you are invading another empire or when making use of a right of passage) they will consume more food than normal. It also depends on the troop type how much food they consume.
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