Problem $2(10$ points$)-$ Efficient Air Conditioners for Arizona

An air conditioner is operating at steady state to maintain a home at $25$C when it is $45$C outside. Heat transfers from the outside environment into the interior of the home at a rate of $10$ kW $.$ An inventor claims that they have created an air conditioner that can accomplish this objective while only consuming a new power input of $2$ kW $.$

a$.$ For the above scenario, what is the maximum coefficient of performance for an air conditioner that obeys the laws of thermodynamics?

b$.$ Is it thermodynamically possible to accomplish the above objective while only consuming $2$ kW of power? Be sure to justify your answer using an appropriate calculation$($s$).$

c$.$ What is the coefficient of performance for the air conditioner that the inventor claims to have created?