  Given a system with a finite heat capacity and a heat reservoir, and two
values of initial temperatures, $T_+$ and $T_- (< T_+)$, we enquire, in which
case the optimal work extraction is larger: when the reservoir is an infinite
source at $T_+$ and the system is a sink at $T_-$, or, when the reservoir is an
infinite sink at $T_-$ and the system acts as a source at $T_+$? It is found
that in order to compare the total extracted work, and the corresponding
efficiency in the two cases, we need to consider three regimes as suggested by
an inequality, the so-called arithmetic mean-geometric mean inequality,
involving the arithmetic and the geometric means of the two temperature values
$T_+$ and $T_-$. In each of these regimes, the efficiency at total work obeys
certain universal bounds, given only in terms of the ratio of initial
temperatures. The general theoretical results are exemplified for thermodynamic
systems for which internal energy and temperature are power laws of the
entropy. The conclusions may serve as benchmarks in the design of heat engines,
where we can choose the nature of the finite system, so as to tune the total
extractable work and/or the corresponding efficiency.
