Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.
$$f ( x , y , z ) = 14 x + 8 y + 12 z , x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 101$$
A) $f ( 14,8,12 ) = 404$
B) $f ( 20,9,18 ) = 568$
C) $f ( 7,4,6 ) = 202$
D) $f ( 18,17,5 ) = 308$
E) $f ( 8,4,12 ) = 212$

Question

Quizplus · Accepted Answer

Using Lagrange multipliers, the maximum value of the function $f(x, y, z) = 14x + 8y + 12z$ subject to the constraint $x^2 + y^2 + z^2 = 101$ is found when $x = 7$, $y = 4$, and $z = 6$, giving $f(7, 4, 6) = 202$.

Use Lagrange Multipliers to Find the Maximum Value of the Function