Use Lagrange Multipliers to Solve the Problem $f ( x , y ) = x y$

Multiple Choice

Use Lagrange Multipliers to solve the problem.
Find the maximum value of $f ( x , y ) = x y$ subject to $x + 2 y = 80$ .

A) $f _ { \max } = 800$
B) $f _ { \max } = 40$
C) $f _ { \max } = 400$
D) $f _ { \max } = 2$
E) $f _ { \max } = 10$