An engineer designs a cyclic heat engine operating between a hot reservoir at absolute temperature \(T_H\) and a cold reservoir at absolute temperature \(T_C\). In each cycle, the engine absorbs a fixed quantity of heat \(Q_H\) from the hot reservoir. To maximize the net work output \(W\) per cycle, the engineer considers two potential modifications:

Modification 1: Increase the hot reservoir temperature to \(T_H + \Delta T\).
Modification 2: Decrease the cold reservoir temperature to \(T_C - \Delta T\).

Assuming both modified engines operate at maximum theoretical Carnot efficiency, which modification produces a greater increase in net work output per cycle, and why?