SOLUTION: There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional tree planted in the orchard, the output per tree drops by 10 apples. How many trees shoul

Question 534157: There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional tree planted in the orchard, the output per tree drops by 10 apples. How many trees should be added to the existing orchard in order to maximize the total output of trees ?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional tree planted in the orchard, the output per tree drops by 10 apples. How many trees should be added to the existing orchard in order to maximize the total output of trees ?
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# apples = (50+x)(800-10x)
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# = (40000-500x+800x-10x^2)
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# = -10x^2 +300x + 40000
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# = -x^2 + 30x + 4000
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Max occurs when x = -b/(2a) = -30/(-2) = 15
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15 trees should be added
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Cheers,
Stan H.
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