I was solving following question related to lagrange multipliers
Find absolute extreme values of $f(x,y,z)=z$ subject to the constraints $x^2+y^2=z^2$ and $x+y+z=24$
By the method of lagrange multipliers I got two values of $f$, $ z=\frac{48}{2+\sqrt2},\frac{48}{2-\sqrt2}$,where one would be absolute minima and other absolute maxima.
But our constraints form a non-bounded region so we can't guarantee the existence of absolute maxima and minima.So my question is Do we have any of the two(abs maxima and minima) in this question?
