Fruit tree output varies from year to year; can you plan ahead? Part I

Calculus Level 1

You have recently purchased an orchard and it can hold 200 peach trees. Unfortunately, all of the trees are infested with bugs and need to be cut down. You decide to replant, and learn that peach trees have the following characteristics:

  • for the first 4 years, peach trees produce no fruit.
  • for years 5-20, peach trees produce 5 bushels / year
  • after year 20, peach trees no fruit

How often should you plan on replanting new trees to maximize peach production over the next 100 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)?

Details and assumptions

If you are interested in optimization problem, you might want to look at Part Two of this problem.


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