(adsbygoogle = window.adsbygoogle || []).push({}); 1a) Determine the maximum value of f(x,y,z)=(xyz)^{1/3}given that x,y,z are nonnegative numbers and x+y+z=k, k a constant.

1b) Use the result in (a) to show that if x,y,z are nonnegative numbers, then (xyz)^{1/3}< (x+y+z)/3

Attempt:

1a) Using the Lagrange Multiplier method, I get that the absolute maximum of f subject to the constraints x+y+z=k and x,y,z>0 is k/3

1b) Here, it seems to me that one of the constraints, namely x+y+z=k, is removed. If so, then how can we still use the result of part (a) here?

I need some help on part (b). Any help is appreciated!

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# Homework Help: Global optimization subject to constraints

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