Question 1101747: Assume x and y are positive numbers. If xy = 1/9, what is the smallest possible sum of 60x and 135y?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Assume x and y are positive numbers. If xy = 1/9, what is the smallest possible sum of 60x and 135y?
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S(x) = 60x + 135(1/9x)
S(x) = 60x + (135/9)(1/x)
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S'(x) = 60 + (135/9)[-1/x^2]
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Solve for "x"::
S'(x) = 0
60 = (135/9)(1/x^2
x^2 = 135/(9*60)
x^2 = 135/(540)
x^2 = 0.25
x = 0.5
==
Solve for y
y = (1/(9*x) = (1/(9*0.5)) = (1/4.5)
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Sum = 60x + 135y
Sum = 60*0.5 + 135(1/4.5) = 30 + 30 = 60
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Cheers,
Stan H.
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