A monopolist is currently and successfully practicing $3$rd$-$degree price discrimination across two groups of consumers with the following demand functions: $1(1)=4290\mathrm{.}61$

and $2(2)=2760\mathrm{.}32$

$.$ Their current production facility has $()=12,300+138$

where $=1+2$

$.$

The monopolist feels that the facility is getting old and would like to move to another facility that has lower fixed costs $()=8,800+279$

$.$ They have asked you to make a recommendation: should they switch to the newer facility or stay at their current one? Your recommendation must be supported by an explanation and numerical evidence.