Hypothetically even if the tree did produce one mature coconut per day you would need more than that. You would still need another food source, coconuts are lacking in vitamins and protein, for long term health a coconut is just not sufficient. You would have the benefit of some liquid you could drink but like they show in Castaway, coconut juice IS a natural laxative. One cool thing about coconuts is you can use their shells (if they weren't obliterated from you opening them) as bowls and containers.
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