Since y and z can be negative and x positive it's possible for x+2y+2z=108, and to make xyz as large as you want. For example, take x=108+t, y=-t/4=z. Then x+2y+2z=108 for all t values, and as t goes to infinity, so does f(x(t),y(t),z(t)=(108+t)(-t/4)(-t/4)= (108+t)(t/4)(t/4)
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