An apple grower finds that if he plants 80 trees per acre, each tree will yield 26 bushels of fruit. He estimates that for each additional tree planted per acre, the yield of each tree will decrease by 4 bushels. Given a price of $1.00 per bushel, find the maximum revenue and how many trees he should plant per acre to maximize his harvest.

Question

Mathematics

Amiah Le

7 January, 21:24

An apple grower finds that if he plants 80 trees per acre, each tree will yield 26 bushels of fruit. He estimates that for each additional tree planted per acre, the yield of each tree will decrease by 4 bushels. Given a price of $1.00 per bushel, find the maximum revenue and how many trees he should plant per acre to maximize his harvest.

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Answers (1)

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Jacob Baldwin · Answer 1

Answer: The maximum revenue is $7482. To get a maximum yield, The number of trees per acre needed is 43.

Step-by-step explanation:

Solution:

Let x represent the extra tree

So for an additional tree the yield of each tree will decrease by 4 bushels.

(80 + x) (26-4x) by expanding

2080 - 320x + 26x - 4x^2

Using x = - b/2a

X = 294 / - 8

X = - 36.75

So apparently he currently has far too many trees per acre. To get the maximum yield, she needs to reduce the number of trees per acre by 36.75

So the number of trees per acre for maximum yield is

80-36.75

=43.25

Approximately x=43

So by reducing he get extra bushel in the tune of 174.

Total revenue = 174 * 43 * 1$

=$7482