Use Lagrange multipliers to find the indicated extrema of subject to two constraints. In each case,

Use
Lagrange multipliers to find the indicated extrema of ƒ subject
to two constraints. In each case, assume that x, y, and z are
nonnegative.

Maximize ƒ(x, y, z) = xyz

Constraints: x + y + z = 32, x - y + z = 0