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

Multiple Choice

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) $f \left( \frac { 3 } { 2 } , \frac { 9 } { 2 } \right) = \frac { 243 } { 4 }$