The heat supplied by a heat pump used to maintain a building's temperature is often supplemented by another source of direct heat. The fraction of the total heat required that is supplied by supplemental heat increases as the temperature of the environmental air (which serves as the low temperature sink) decreases.
To minimize the total supplemental and heat pump energy required to service the building;
1. What would you choose as the supplemental heat
2. Develop the function of COP of this heat pump with the supplemental heat you chose in 1. to show the increase in the energy efficiency.