A farmer finds that if she plants 60 trees per acre, each tree will yield 45 bushels of fruit. she estimates that for each additional tree planted per acre, the yield of each tree will decrease by 4 bushels. how many trees should she plant per acre to maximize her harvest?

Question

Mathematics

Cale Dougherty

21 January, 23:13

A farmer finds that if she plants 60 trees per acre, each tree will yield 45 bushels of fruit. she estimates that for each additional tree planted per acre, the yield of each tree will decrease by 4 bushels. how many trees should she plant per acre to maximize her harvest?

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Answers (1)

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Darius · Answer 1

Answer: 60 trees

Explanation:

Even if there are trees planted per acre, the decrease of yield of each tree is significant enough to make it less worthwhile to have more trees than less.

In other words, when she plants 60 trees per acre, she gets 2700 bushels of fruit per acre, because 45 bushels per tree = 45 • 60 = 2700. If you plant another tree, you get the equation 41 • 61 = 2501 because there are 4 less bushels per tree. 2501 < 2700 so 60 per acre would maximize the harvest.