An operations 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 $0\mathrm{.}11,\mathrm{.}40,$ and $0\mathrm{.}49,$ respectively. She has scored one potential outsourcer, Ling Services, on each of the factors using a scale of $0-100.$ Ling Services received a score of $40$ for factor A$,60$ for factor B$,$ and $60$ for factor C$.$ What is the factor$-$rating score for Ling Services? $($Round answer to one decimal place.$)$

$160$

$57\mathrm{.}8$

$50\mathrm{.}2$

$69\mathrm{.}4$

$45\mathrm{.}8$