Solve the following problem:
Q: A Carnot heat engine receives heat at 750 K and rejects the waste heat to the environment at 300 K. The entire work output of the heat engine is used to drive a Carnot refrigerator that removes heat from the cooled space at -15°C at a rate of 400 kJ/min and rejects it to the same environment at 300 K. Determine
(a) The rate of heat supplied to the heat engine and
(b) The total rate of heat rejection to the environment.