A reversible heat engine receives heat from a reservoir at 660°C at a rate of 10kW and rejects the waste heat to the ambient air at −9°C. One-half of the work output of the heat engine is used to drive a heat pump which maintains an auditorium at 25°C. The coefficient of performance of the heat pump is 50% of the maximum possible value (i.e. COPHP,max) and it extracts heat from the same ambient air (at −9°C) to which heat engine is rejecting its heat. Draw a schematic of the combined system and determine 1) the coefficient of performance of the heat pump 2) the rate of heat transfer to the auditorium. 3) the rate of heat removal from the ambient air by the heat pump 4) the rate of heat rejection by the heat engine