An hoerations manager is performing a factor$-$rating analysis to help her choose an outsourcing provider. She is focusing on three factors: A$,$ B$,$ and C$,$ with weights of $0\mathrm{.}30,0\mathrm{.}20,$ and $0\mathrm{.}50,$ respectively. She has scored one potential mutsiouncer, Ling Services, on each of the factors using a scale of $10-50.$ Ling Services received a score of $30$ for factor A $46$ for factor B$,$ and $22$ for factor C$.$ What is the factor$-$rating score for Ling Services?

A $98\mathrm{.}0$

$821\mathrm{.}8$

C $32\mathrm{.}7$

D $30\mathrm{.}8$

E $29\mathrm{.}2$