Making an Island/Facilities/Food
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If you do not live on the island permanently and have a main base on another land, it would be more practical to send routine supplies to the island rather than attempt any of the following.
[edit] Food Producing Plants
Freshwater Plants
You're going to have to keep the plants away from the saltwater that your island is probably floating in. One solution is to plant these above the ground, and you're also going to have to give them some of the salt free drinking water for them to survive. If the island has no native soil then it will be required to either import it or generate it from raw materials. Hydroponics is another option.
Saltwater Plants
Edible marine plants include the seaweed kelp and the red alga carrageenan.
[edit] Fishing
Fish: Fish are the most available source of meat for an island. Although means of cooking them would be less readily acquired. Sushi is an alternative, combining farmed seaweed and raw fish. Shellfish can be gathered in large amounts by use of cages and traps.