Publixz Supermarkets use both cashiers and baggers to serve customers at check out. During the first $6$ hours of each workday $($Monday$-$Friday$),5$ cashiers and $2$ baggers serve approximately $19$ customers per hour. A cashier and a bagger who require approximately $5$ minutes at checkout and $3$ minutes at bagging serve each customer. What is the utilization of the Cashier?

$31\mathrm{.}67\%$

$67\mathrm{.}31\%$

$47\mathrm{.}5\%$

$56\mathrm{.}16\%$