  We revisit J. Shallit's minimization problem from 1994 SIAM Review concerning
a two-term asymptotics of the minimum of a certain rational sum involving
variables and products of their reciprocals, the number of variables being the
large parameter. Properties previously known numerically, most importantly, the
existence of the constant in the asymptotics, are proved. We supply a sharp
remainder estimate to the originally proposed asymptiotic formula. The proofs
are based on the analysis of trajectories of a planar discrete dynamical system
that determines the point of minimum.
