Q$3.[10+8=18$ points$]$ Consider the ideal $($Camot$)$ heat engine shown below. If the heat engine rejects $85$ kW of heat $($rate of heat rejection$)$ at the low temperature reservoir, find:

$($a$)$ The heat input rate $($from high temperature reservoir$)$ required to operate the engine.

$($b$)$ Power output of the engine.