Use Lagrange Multipliers to solve the given problem.
Find the maximum value of $f ( x , y ) = x y$ subject to $2 x + y = 60$ .

A) $f _ { \max } = 10$
B) $f _ { \max } = 450$
C) $f _ { \max } = 30$
D) $f _ { \max } = 2$
E) $f _ { \max } = 225$

Question

Use Lagrange Multipliers to solve the given problem.  
Find the maximum value of $f ( x , y ) = x y$ subject to $2 x + y = 60$ .
 
A) $f _ { \max } = 10$
B) $f _ { \max } = 450$
C) $f _ { \max } = 30$
D) $f _ { \max } = 2$
E) $f _ { \max } = 225$

Quizplus · Accepted Answer

The maximum value of $f(x,y)$ occurs when $x=15$ and $y=30$, so $f_{\max}=15\cdot30=450$.

Use Lagrange Multipliers to Solve the Given Problem f(x,y)=xyf ( x , y ) = x yf(x,y)=xy

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