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 .