math

When 300 apple trees are planted per acre, the annual yield is 1.6 bushels of apples per tree. For every 10 additional apple trees planted, the yield reduces by 0.01 bushel per ten trees. How many apple trees should be planted to maximize the annual yield?

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  1. number of groups of 10 extra trees ---- n
    yield = 1.6 bushels per tree or 16 bushels per 10 trees
    now:
    number of groups of 10 trees = 30 , yield = 30(16) = 480 bushels

    after change:
    number of trees in groups of 10 = 30 + n
    yield per 10 tree = .01 - n bushels per 10 trees
    yield = (30+n)(16 - .01n) = 480 + 15.7nn - .01n^2
    d(yield)/dn = 15.7 - .02n = 0 for a max of yield
    .02n = 15.7
    n = 785
    So they should plant 7850 extra trees !!!!

    The drop in yield is really small, I am certain there is a typo somewhere.
    Fix your question, the just change the numbers.

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    Reiny
  2. I had the same problem. Maybe it is 0.01 bushel per ONE tree.

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    Damon
  3. 950 trees (:

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