A heat engine operates between two reservoirs at 850C and 20C. One -half of the work output of the heat engine is used to drive a Carnot heat pump that removes heat from the cold surroundings at 2C and transfers it to a house maintained at 22C. If the house is losing heat at a rate of 20 kJ/s, determine the minimum rate of heat supply to the heat engine required to keep the house at 22C.