A heat engine operates between two reservoir at 800 and 20ºC. One-half of the work output of the heat engine is used to drive a Carnot heat pump that removes heat from the cold surrounding at 2ºC and transfers it to a house maintained at 22ºC. If the house is losing heat at a rate of 62,000 kJ/h, determine the minimum rate of heat supply to the heat engine required to keep the house at 22ºC.