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I need to find the maximum of the function $\ f(x,y,z) = y $ on the following closed set :

$\ y^2+x^2 + z^2 = 3 $

$\ y+ x + z=1$

But I don't have a clue on how to do it ...

Trivially i can get that

$\ 0 < \max(f) < \sqrt{3} $.

Can you give me some pieces of advice on how to solve this kind of problem .

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    Are Lagrange Multipliers a tool you can use? More simply one can use the geometry.2011-12-18
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    no i cant use lagrange multipliers...2011-12-18
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    your trivial is not correct because $3^{1/2}$ does not satifies in $y+x+z=1$2011-12-18
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    Your $f$ is simple. Take the $y$-axis pointing up. Stare at the $x,y,z$ system so that the plane appears as a line and the $y$ axis is pointing up. You are trying to find the height of the point of intersection of a line with a circle.2011-12-18

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