A $286-$room upscale hotel supplies each guestroom with a $1$ oz$.$ bar of facial soap, packed $288$ per case, and a $2$ oz$.$ bar of bath soap, packed $144$ per case. The ending inventory for the month of February was $8$ cases of facial soap $(288$ per case$)$ and $12$ cases of bath soap $(144$ per case$).$ Twelve $(12)$ cases of facial soap $(288$ per case$)$ and fifteen $(15)$ cases of bath soap $(144$ per case$)$ were purchased and received in March, while the hotel ended March with seven $(7)$ cases of facial soap $(288$ per case$)$ and ten $(10)$ cases of bath soap. $6,297$ room nights $(71\mathrm{.}0\%$ occupancy$)$ were sold in March and $5,842$ room nights are projected for April $(68\mathrm{.}1\%$ occupancy$).$ What is the usage factor for the bath soap?

Group of answer choices

$\mathrm{.}595$

$\mathrm{.}246$

$\mathrm{.}389$

$\mathrm{.}332$