Find the Indicated Maxima or Minima $f(x, y, z)=x y+z$ , Subject To

Multiple Choice

Find the indicated maxima or minima.
-Maximum of $f(x, y, z) =x y+z$ , subject to $x^{2}+y^{2}+z^{2}=1$

A) 1 when $x=1, y=1, z=0$
B) 1 when $x=0, y=0, z=1$
C) 1 when $x=1, y=1, z=1$
D) 1 when $x=0, y=1, z=0$