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

Multiple Choice

Find the indicated maxima or minima.
-Maximum of $f(x, y) =x y$ , subject to $x+y=100$

A) 0 when $x=0, y=100$
B) 100 when $x=50, y=50$
C) 2500 when $x=50, y=50$
D) 0 when $x=100, y=0$