Use Lagrange Multipliers to Find the Given Extremum $x$ And $y$ Are Positive

Multiple Choice

Use Lagrange multipliers to find the given extremum. In each case, assume that $x$ and $y$ are positive. Maximize $f ( x , y ) = x y$ Constraint $x + y = 10$

A) $f ( 7,3 ) = 21$
B) $f ( 5,5 ) = 25$
C) $f ( 6,4 ) = 24$
D) $f ( 2,8 ) = 16$
E) $f ( 1,9 ) = 9$