Use Lagrange multipliers to find the maximum value of f (x,y)= 9xy subject to the constraint 9x + 3y = 27.
A)f (0,0)= 0
B)f (3,9)= 243
C) $f \left( \frac { 3 } { 4 } , \frac { 9 } { 4 } \right) = \frac { 243 } { 16 }$
D) $f \left( \frac { 3 } { 2 } , \frac { 9 } { 2 } \right) = \frac { 243 } { 4 }$

Question

Quizplus · Accepted Answer

Using Lagrange multipliers, we set up the system: ∇f = λ∇g, where g(x, y) = 9x + 3y - 27. Solving, we find the critical point $(\frac{3}{2}, \frac{9}{2})$, which gives the maximum value of $\frac{243}{4}$.

Use Lagrange Multipliers to Find the Maximum Value of F f(34,94)=24316f \left( \frac { 3 } { 4 } , \frac { 9 } { 4 } \right) = \frac { 243 } { 16 }f(43​,49​)=16243​

Use Lagrange Multipliers to Find the Maximum Value of F $f \left( \frac { 3 } { 4 } , \frac { 9 } { 4 } \right) = \frac { 243 } { 16 }$