Question 101813: The crop yield, Y, (in bushels) for various amounts, x (in pounds per 100 square feet) of fertilizer used in 18 different plots of land is as shown in the table below. The graph of the data can be modeled by Y(x)=-0.017x^2+1.0765x + 3.8939.
Plot / Fertilizer (x) / Yield - Y(x)
1 0 4
2 0 6
3 5 10
4 5 7
5 10 12
6 10 10
7 15 15
8 15 17
9 20 18
10 20 21
11 25 20
12 25 21
13 30 21
14 30 22
15 35 21
16 35 20
17 40 19
18 40 19
based on the data and the quadratic model, what is the optimal amount of fertilizer to apply for maximum crop yield? Explain or show how you decided.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The crop yield, Y, (in bushels) for various amounts, x (in pounds per 100 square feet) of fertilizer used in 18 different plots of land is as shown in the table below. The graph of the data can be modeled by
Y(x)=-0.017x^2+1.0765x + 3.8939
What is the optimal amount of fertilizer to apply for maximum crop yield?
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The max crop yield occurs when x=-b/2a = -[1.0765]/[-2*0.017] = 31 lbs per 100
square feet)
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Cheers,
Stan H.
Explain or show how you decided.
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