This question is a generalized variant of: Hardness of perimeter minimization?Given $xyz=C$ where $x, y,$ and $z$ are integer variables and $C$ is integer constant. Assume all integers are encoded in binary.What is the complexity of finding $x, y, z$ such that $xy+xz+yz$ has minimum value? Is there any subexponential algorithm that solves this problem? Does the problem become easier when integers are encoded in unary?Edit Motivation: I'm interested in the following generalized problem:Input: intgers $C$ and $K$Problem: Find integers $x$, $y$, and $z$ such that $xyz\ge C$ and $xy+xz+yz\le K$
Hardness of geometric area minimization problem
cc.complexity theory