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In This War Of Mine, Food is needed for the Survivors to stay alive. A survivor needs to eat every two days or so at minimum to stay nourished. Being hungry, very hungry or starving sharply reduces the chances that a character will regain healthy status if they have been resting to recover from the slightly wounded or slightly sick statuses, reduces combat effectiveness in defending the shelter at night, and causes the character to complain about needing food or being hungry. A character can eat either canned food, which is the best option and requires no additional effort to prepare; cooked meals, the standard option and more economical than eating canned food constantly but requiring cooking at the stove in addition to fuel and water; or finally they can eat raw meat or raw vegetables, which are edible unprepared but less nourishing than prepared food (please confirm exact effects. I believe that people will return to hungry status sooner than if they had eaten prepared meals instead) food management is one of the most important elements of the game; strategic thought is required to make the most of your limited supplies.
Food is one of the highest priorities to take home when scavenging, second only to medical supplies in importance and value. While you won't be taking anywhere near as much home as wood or components, but you should still try to make sure you take home full stacks at a time to avoid wasting space in your inventory. Food items are most often found in fridges which often yield more than half the food in a location in a single scavenging pile, but if possible try to search out the other, more random spawns to combine them. Food is valuable enough to attract other scavengers as well; if there are NPC scavengers in a location, they will take food items from scavenging locations until they either leave by scripting or are stopped by player interaction (which is to say, when you fire upon them) If you find yourself competing with other scavengers at a location, immediately grab all the food, medical supplies, valuables or unique items at the expense of wood and components or any other low-value items, even if you have need of the lower-value building supplies. Building supplies will mostly still be there later- food and medicine will likely not be.
The best way to eat food is to have a cooked meal consisting of both meat and vegetables every second day. This keeps your people either neutral or hungry, but they shouldn't drop to very hungry or starving if you're punctual. If they do drop to very hungry or starving, they will take a meal per level of hunger to recover. It is possible to feed someone when they're not hungry, which grants them the well-fed trait which presumably improves their healing and guarding abilities, but is expensive and unneeded, though if there isn't anything else you can do for someone who is in dire straits, it may improve their survivability and keep them alive until you can muster up the bandages or medications they need.
Bruno is the best character to cook with, as he acts as though your stove is improved even if it isn't and uses less fuel and water than others would, but you can upgrade the stove if you don't have him and other people will cook food as efficiently as Bruno would have (no method exists to get the bonuses he gets at the moonshine still or herbal workshop without him, unfortunately) food is producible, to a point, the upgraded version of the herbal garden is the vegetable garden, which allows the growth of up to eight vegetables every three days if provided water and a little fertilizer, and traps for small animals (read: rats) can be manufactured and placed which generate two raw meat from either one raw meat, one canned food, or one fertilizer. You may only build two traps, regardless of whether you can afford to produce more, per playthrough, and combined they produce about one third of your food needs depending on how many survivors you have to feed. Anton's special ability allows traps to cycle more quickly, making them more useful still.
IMPORTANT NOTE: this information is potentially incomplete/inaccurate. Additional confirmation is required.