Consider a Carnot heat$-$pump cycle executed in a steady$-$flow system in the saturated liquid$$vapor mixture region using refrigerant$-134$a flowing at a rate of $0\mathrm{.}180$ kg$/$s as the working fluid. It is known that the maximum absolute temperature in the cycle is $1\mathrm{.}2$ times the minimum absolute temperature, and the net power input to the cycle is $5$ kW$.$ If the refrigerant changes from saturated vapor to saturated liquid during the heat rejection process, determine the ratio of the maximum to minimum pressures in the cycle. $($Round the final answer to three decimal places.

The ratio of the maximum to minimum pressures in the cycle is