SOLUTION: An orchard contains 30 apple trees, each of which yields approximately 400 apples over the growing season. The owner plans to add more trees, but the guys at Texas A&M advise tha

Question 417894: An orchard contains 30 apple trees, each of which yields approximately 400 apples over the growing season.
The owner plans to add more trees, but the guys at Texas A&M advise that because of crowding, each new tree will reduce the average yield per tree by about 10 apples over the growing season.
How many trees should be added to maximize the total yield of apples, and what is the maximum yield?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
An orchard contains 30 apple trees, each of which yields approximately 400 apples over the growing season.
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The owner plans to add more trees, but the guys at Texas A&M advise that because of crowding, each new tree will reduce the average yield per tree by about 10 apples over the growing season.
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How many trees should be added to maximize the total yield of apples, and what is the maximum yield?
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Total yield = [(30+x) trees][(400-10x)apples]
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TY = 30*400 - 300x+400x - 10x^2
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TY = -x^2+10x+1200
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Max occurs when x = -b/(2a) = -10/(2*-1) = 5 trees (# of trees to add)
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TY(5) = -5^2+10*5 + 1200 = 1225
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Cheers,
stan H.
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Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = number of trees to be added
Let = yield from orchard

The maximum of a quadratic is at

5 trees should be added to maximize yield
The yield, , is

Here's a plot:

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