Prismatic Package

Calculus Level 2

It is given a prismatic package which sides measure \(x,y,z\) such that its volume is \(108\). Its surface (without the cover) is given by the equation: \( S = xy + 2yz + 2xz \)

Setting \(x,y,z\) as variables, what is the value of \(x+y+z\) if we want to minimize the surface area of the package?

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