Yahoo Answers: Answers and Comments for Optimization Problem? [Mathematics]
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From Sydnei
enCA
Mon, 30 Mar 2020 00:59:47 +0000
3
Yahoo Answers: Answers and Comments for Optimization Problem? [Mathematics]
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From Philip: Put numbers = x & (102x).
Put f(x) = x(10...
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Mon, 30 Mar 2020 06:27:42 +0000
Put numbers = x & (102x).
Put f(x) = x(102x)^2 = x(x102)^2 = x[x^2 204x + a^2], where a = 102.
Then f(x) = x^3 204x^2 + a^2x.
f'(x) = 3x^2  408x + a^2.
f''(x) = 6x  408 = 6(x68).
Extremums occur where f'(x) = 0, ie., where x^2 136x + (1/3)[3*34]^2 = 0, ie., where
g(x) = x^2  136x + 3(34)^2 = 0...(1). for g(x) = 0, 2x = 136(+/)D, where D^2 = (136)^2  4*3*(34)^2 = 16(34)^2  12(34)^2 = 4(34)^2. Then D =2*34 =68 and
2x = 136(+/)68 = 68[2(+/)1]. Then x = 34(1 or 3) = 34...(2) or x = 102...(3). Clearly,
root x = 102 is invalid. Therefore x = 34.
At x = 34, f''(x) = 6*34  408 = (408204) = 204, < 0 > extremum at x = 34 is a
maximum.
f(34) = 34(10234)^2 = 34[3*34  34] = 34[2*34] = 2*17[4*17] = 8*(17)^2 = 8*(289) =
8*(2901) = 23208 = 2312.
The 2 numbers are 34 and 68 such that f(34) = maximum = 2312 = 34*68.

From david: n = 1st number
102  n = 2nd number
f(n) = n(1...
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Mon, 30 Mar 2020 01:26:25 +0000
n = 1st number
102  n = 2nd number
f(n) = n(102n)^2 <<< derivative of this
f '(n) = 3(n^2  136 n + 3468)
n^2  136 n + 3468 = 0
(n102)(n34) = 0
n = 34 and n = 102<< not possible, 2ns number would be 0
n = 34 ... 102  n = 68 <<< answers

From sepia: Find two positive real numbers such that they ...
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Mon, 30 Mar 2020 01:20:05 +0000
Find two positive real numbers such that they sum to 102
and the product of the first times the square of the second is a maximum.
x + y = 102
x(y^2) = 101^2
(102  y)y^2 = 101^2
y^3  102y^2 + 101^2 = 0
y = 101 and x = 1

From Krishnamurthy: Find two positive real numbers such that they ...
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Mon, 30 Mar 2020 01:13:17 +0000
Find two positive real numbers such that they sum to 102
and the product of the first times the square of the second is a maximum.
x + y = 102
x(y^2) = 51^3
(102  y)y^2 = 51^3
y^3  102y^2 + 51^3 = 0
y = 51
The two positive real numbers are 51 and 51