The number of apples produced by each tree in an apple orchard depends on how densely the trees are planted. If n trees are planted on an acre of land, then each tree produces 900-9n apples. So the number of apples produced per acre is A (n) = n (900-9n)

Question

Mathematics

Luca Hunt

15 June, 10:47

The number of apples produced by each tree in an apple orchard depends on how densely the trees are planted. If n trees are planted on an acre of land, then each tree produces 900-9n apples. So the number of apples produced per acre is A (n) = n (900-9n)

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Bryanna Merritt · Answer 1

A (n) = n (900 - 9n) = 900n - 9n^2

For maximum A (n), A' (n) = 0

A' (n) = 900 - 18n = 0

18n = 900

n = 900/18 = 50

Therefore, for maximum apples to be produced, 50 trees should be planted per acre.