Solve the problem.
-$\text { Maximize } f ( x , y , z ) = e ^ { 4 x + 9 y + 2 z } \text { subject to } x + y + z = 0 , x + 2 y + 3 z = 0 \text {, and } x + 4 y + 9 z = 0$
A) 0
B) e
C) 1
D) 15

Question

Quizplus · Accepted Answer

The given system of equations can be solved to find the values of $x$, $y$, and $z$. The equations are linear and homogeneous, and they imply that $x = y = z = 0$, since they form a system with a unique solution (the determinant of the coefficients is non-zero). Substituting these values into the function $f(x, y, z) = e^{4x + 9y + 2z}$ gives $f(0, 0, 0) = e^0 = 1$.