There are different ways to increase your food production in all castles and outposts.
2. Build as much public order as you can. the best way to do this is to build parks and castle gardens and fill your castles with these to increase food production.
3. Build a bakery, and level it up to maximum.
4. Build a hunting-lodge which can help you to increase food production.
5. Hire over seers to increase 25% more food production. You can hire over seer from tha tab ‘kings market’
6. If you have a research tower, you can research three field crop rotation, it will further increase food production.
7. Decreasing numbers of dwellings/ town houses in your castles will increase your public order and that will help to increase food production.
8. always get 8 food outposts, these are the best.
And constantly loot food to feed big army.
Hope this helps!