Use Lagrange multipliers to find the maximum value of f (x, y) = 9xy subject to the constraint 9x + 5y = 45.
A)
$f \left( \frac { 5 } { 4 } , \frac { 9 } { 4 } \right) = \frac { 405 } { 16 }$
B)
$f \left( \frac { 5 } { 2 } , \frac { 9 } { 2 } \right) = \frac { 405 } { 4 }$

C) f (5, 9) = 405

D) f (0, 0) = 0

Question

Use Lagrange multipliers to find the maximum value of f (x, y) = 9xy subject to the constraint 9x + 5y = 45.
A) 
$f \left( \frac { 5 } { 4 } , \frac { 9 } { 4 } \right) = \frac { 405 } { 16 }$
B) 
$f \left( \frac { 5 } { 2 } , \frac { 9 } { 2 } \right) = \frac { 405 } { 4 }$

C) f (5, 9) = 405

D) f (0, 0) = 0

Quizplus · Accepted Answer

Using Lagrange multipliers, the maximum value occurs at $x = \frac{5}{2}$ and $y = \frac{9}{2}$, giving $f(x, y) = \frac{405}{4}$.

Use Lagrange Multipliers to Find the Maximum Value of F f(54,94)=40516f \left( \frac { 5 } { 4 } , \frac { 9 } { 4 } \right) = \frac { 405 } { 16 }f(45​,49​)=16405​

Use Lagrange Multipliers to Find the Maximum Value of F $f \left( \frac { 5 } { 4 } , \frac { 9 } { 4 } \right) = \frac { 405 } { 16 }$