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25 August, 11:30

An apple farm yields an average of 43 bushels of apples per tree when 23 trees are planted on an acre of ground. Each time 1 more tree is planted per acre, the yield decreases by 1 bushel (bu) per tree as a result of crowding. How many trees should be planted on an acre in order to get the highest yield?

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  1. 25 August, 11:52
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    Step-by-step explanation:

    Equation of the yield

    Yield = Bushels per tree * number of trees

    Bushels per tree = 43 when the number of trees is 23 and decreases by 1 for each additional tree

    Let n = number of trees

    Bushels per tree = 43 when n = 23.

    So, bushels per tree = (66 - x)

    = (66 - 23)

    = 43

    Yield = (66 - n) * n

    Yield = 66n - n2

    Taking the derivative,

    66 - 2n

    set this to zero to find the maximum 66 - 2n = 0

    2x = 66 and x = 33

    Maximum yield will be given with 33 trees.

    To test 33, 34 and 35 to see that all their yield is less,

    yield = (50 - 35) 35

    = 1085

    yield = (50 - 34) 34

    = 1088

    yield = (50 - 33) 33

    = 1089
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