"Dumping, in economics, is a kind of injuring pricing, especially in the context of international trade. It occurs when manufacturers export a product to another country at a price below the normal price with an injuring effect. The objective of dumping is to increase market share in a foreign market by driving out competition and thereby create a monopoly situation where the exporter will be able to unilaterally dictate price and quality of the product."
How would it work in this example?
The other guy would sell you coconuts and bananas well below the Zone of Possible Agreement (ZOPA), and you would be so glad to buy everything from them -- destroying your industry.
A few years go by, and they raise their prices above the ZOPA -- and you have no option because it would cost you a lot to rebuild your industry from scratch.
If you try to produce bananas, they drop the price of bananas; and make profit from coconuts. If you try to produce coconuts, they drop the price of coconuts, and make profit from bananas. (You need coconuts and bananas!)
That's what happens in real world -- developing countries export iron for $100/ton (2,200 pounds) and buy high value-added products (phones, tablets, computers) for $500/unit.
Rich countries use the profit they make from high value-added products and services to subsidize their farmers, pushing the price of food down. For instance, wheat costs $188.75 per metric ton, less than $0.20 per kg ($0.10 per pound).
Without subsidies, the farming industry would be decimated from rich countries, and prices would go up.
So, "free market" is an abstraction that doesn't exist in the real world -- and you can see it in this idealized model of two islands.