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Lagrange question: f(x,y,z) = x/(1+x) * y/(1+2y) * z/(1 + 3z)
- Thread starter woshifate
- Start date
D
Deleted member 4993
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Suppose that R>0. Find the maximum value of
\(\displaystyle f(x,y,z)= \left(\frac{x}{1+ x}\right)\left(\frac{y}{1+ 2y}\right)\left(\frac{z}{1+ 3z}\right)\)
among all postive numbers x,y,z satisfying x+2y+3z = R
What are your thoughts?
Please share your work with us ...even if you know it is wrong
If you are stuck at the beginning tell us and we'll start with the definitions.
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What are your thoughts?
Please share your work with us ...even if you know it is wrong
If you are stuck at the beginning tell us and we'll start with the definitions.
You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:
http://www.freemathhelp.com/forum/th...Before-Posting
I believe I should be using Lagrange method, but the problem is when finding the derivatives, I could not get the seperate the ratio e.g) x/z = 3(1+3z) / (x+1) and so on
D
Deleted member 4993
Guest
Suppose that R>0. Find the maximum value of
\(\displaystyle f(x,y,z)= \left(\frac{x}{1+ x}\right)\left(\frac{y}{1+ 2y}\right)\left(\frac{z}{1+ 3z}\right)\)
among all postive numbers x,y,z satisfying x+2y+3z = R
Let's define:
g(x,y,z) = 1/f = (1 + 1/x)(1 + 1/y) (1 + 1/z)
The maximum value of 'f' will be related to the minimum value of 'g'.
continue...