Posted by admin | Posted in trees,shrubs | Posted on 01-12-2010
Tags: apple trees michigan, apple trees michigan deer, apple trees michigan sale, collaboration, food, gardening, growing apple trees michigan, marketing, planting apple trees michigan, web2.0
College ALgebra Problem?
Hi I am confused on a problem and the setup of it.
From past surveys and records, an orchard owner in northern Michigan has determined that if 26 apple treees per acre are planted, each tree yields 500 apples, on average. The yield decreases by 10 apples per tree planted. How many trees should be planted per acre to acheive the maximum total yield?
I am thinking the equation I need to optimize is 26 x^2 – 10 x + 500. This is totally wrong as I am not getting the correct answer in the back of the back when I maximize. Any help would be great!! Thanks
When there are 26 trees per acre, there are 500 apples/tree
For each tree added (26 + x) the yield decreases by 10 apples (500 – 10x)
f(x) = (26 + x)(500 – 10x)
f(x) = 1300 + 240x – 10x^2 <- so your equation is wrong.
f'(x) = 240 - 20x
240 - 20x = 0
20x = 240
x = 12
So when there are 38 trees, there are 380 apples per tree, for a total of 14,400 apples per acre
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