Maximize xyz on a plane

MediumCalculus~4m

Maximize xyzxyz subject to x+y+z=cx+y+z=c with x,y,z>0x,y,z>0. For c=3c=3, what is the maximum value of xyzxyz?

Show hints (2)+
  1. By symmetry the optimum is x=y=zx=y=z.
  2. Equivalent to AM–GM.

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Asked at: Citadel

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