Question 184126: An orange grower finds that she gets a yield of 40 bushels of oranges per tree when she plants 20 trees on an acre of ground. However, the yield decreases by 1 bushel per tree for each additional tree she plants on the acre due to crowding. How many trees should she plant per acre to maximize her yield?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An orange grower finds that she gets a yield of 40 bushels of oranges per tree when she plants 20 trees on an acre of ground. However, the yield decreases by 1 bushel per tree for each additional tree she plants on the acre due to crowding. How many trees should she plant per acre to maximize her yield?
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Yield = (# of trees)(# of bushels)
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Y(x) = (20 + x)(40-x)
Y(x) = 800 +20x-x^2
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The maximum yield occurs when x = -b/2a = -20/(2*-1) = 10
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Number of trees should be 20+x = 30
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Cheers,
Stan H.
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