Q$2$: The aim is to minimize the compressor power while maintaining a constant coefficient of performance $)=(2.$ What are the optimal temperatures for the condenser and evaporator? Additionally, calculate the power consumption of the compressor. The performance characteristics of the evaporator and condenser heat transfer are:

$Q_e=12\mathrm{.}5+0\mathrm{.}2T_e+0\mathrm{.}001T_e^2-0\mathrm{.}05T_c-0\mathrm{.}0005T_c^2$

$P_{\text{c}\text{o}\text{m}\text{p}}=3+0\mathrm{.}01T_c+0\mathrm{.}005T_e{T}_c+0\mathrm{.}06T_e$