Given a sequence of number $r_i$, what kind of $x_i$ would maximize $ \frac{\sum x_i r_i}{|x_i|}$
My intuition is that the solution is when $x_i = k r_i$ for a constant $k$. But I cannot prove it.
I have been trying to rearrange it to form a Cauchy inequality because the numerator is a dot product..but so far no luck... The absolute value signs are hard to handle..