You have recently purchased an orchard and it can hold 100 apple trees. Unfortunately, all of the trees are currently too old and are past the age of bearing fruit. You decide to replant, and learn that apple trees have the following characteristics:
- they must grow for two years before they begin bearing fruit.
- from years 3-10 they bear fruit at a rate of 10 bushels / year
- from years 11-12 they bear fruit at a rate of 9 bushels / year
- from years 13-20, they bear fruit at a rate of 8 bushels / year
- After year 20, the trees bear no fruit at all.
How often should you plan on replanting new trees to maximize apple production over the next 60 years? (note that fractional years are not an option, since you'd miss the harvest if the trees aren't present for a full year)?