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

Calculus Level 2

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)?

Every 15 years Every 12 years Every 10 years Every 20 years

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1 solution

Vikram Chugh
Jan 31, 2014

for after 10 years:- 10 * 8 = 80 * 6 = 480

for after 12 years:- 10 * 8 = 80 + (2 * 9) = 98 * 5 = 490

for after 15 years:- 10 * 8 = 80 + (2 * 9) = 98 + (3 *8 ) = 122 * 4 = 488

for after 20 years:- 10 * 8 = 80 + (2 * 9) = 98 + (8 *8 ) = 162 * 3 = 486

This is not how it should be solved... I hate multiple choice

Patrick Engelmann - 7 years, 4 months ago

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How should it be solved then? Post your solution.

Carl Araya - 7 years, 1 month ago

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Use calculus. Or, you can like me, plot your graph on geogebra?

Julian Poon - 6 years, 11 months ago

Could you specify why 8 and 10??? 8 minimum number of aples and 10 for every 10 appple trees???

Yuliya Skripchenko - 7 years, 4 months ago

1 0 0 2 0 0 3 10 3.33 4 20 5 5 30 6 6 40 6.66 7 50 7.142 8 60 7.5 9 70 7.77 10 80 8 11 89 8.09 12 98 8.16 13 106 8.15 14 114 8.14

Nikunj Lakhani - 7 years, 4 months ago

maximum apple production in 11-12 yrs is 9 bushels so that after next 60 yrs we get 9*50=540 .hence ans is 12 yrs.

Ankit Soni - 7 years, 4 months ago

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