A Carnot engine operates between temperature levels of $397$C and $7$C and rejects $20$ KJ$/$min to the environment.

The total network output of the engine is used to drive heat pump which is supplied with heat from the environment at $7$C and rejects heat to a home at $40$C$.$

Determine:

a$)$ the net work delivered by the engine in KJ$/$min

b$)$ the heat supplied to the heat pump in KJ$/$min

c$)$ the overall COP for the combined devices which is defined as the energy rejected to the home divided by the initial energy supplied.