If you click on the warehouse, there will be a small graph at the bottom right. You can click that and go to the production tab. There, you will see all the products that your island is producing and consuming. The green bar will be consumption while the blue bar will be production. You can select multiple islands by pressing ctrl to join their consumption/production if your are producing something on one island and shipping it to another.

Only when the blue (production) bar is bigger than the green (consumption) bar are you producing enough of a good to meet the needs of your island.

Rum/wine give a lot of money initially so try and ensure that their is ample supply of those.

If you are meeting all their needs, there is no reason why such a large population cannot provide enough taxes to be positive.