Suppose we have a collection of fixed vectors $a,b,c \in \mathbb{R}^3$ and we add another vector $x \in \mathbb{R}^n$ to each of the fixed vectors. How does one maximise the sum of their norms, as in the following expression: $|a + x| + |b + x| + |c + x|$?
My first instinct is this is a classic vector classic/optimization problem, but my heads not stuck on right and I can't quite figure it out.