$(25$ points$)$ The elementary gas phase reaction $AB$ takes place in a PFR at constant temperature and pressure with a conversion of $58\%.$ Your supervisor proposed to put a CSTR upstream of this PFR$.$ Calculate $x_1($conversion at the exit of the CSTR$)$ and $x_2($conversion at the exit of the PFR$)$ after this modification if the volume of the CSTR is half of the PFR$.$ All other variables such as temperature and flow rates remain constant.