A house located in a city with an outside air temperature of $-3$ deg C is heated with a CARNOT heat pump and maintained at an indoor air temperature of $27$ deg C$.$ The heat loss of the house is $45$ kW$.$ The energy required for the heat pump is provided by a heat engine operating between a $377$deg C source and $-3$deg C sink$.$ The thermal efficiency of the heat engine is nth $=0\mathrm{.}35.$

a$)$ Calculate the heat Qu absorbed from the source at $377$ deg C$.$

b$)$ Find the net waste heat released to the environment at $-3$ deg C $($by the heat pump and engine$).$