Problem $1(30$ points$)$

To comply with the city's safety protocol amid COVID spike, Tommy's Taco Shop accepts only take$-$out orders. Customers first place their order and pay on$-$line. The shop has five cooks, three assemblers, and two baggers who complete the order by bagging it$,$ labeling the bag with the recipient's name and placing the bag in a pickup area. It takes on average $6$ minutes to cook, and $2$ minutes to assemble an order. Bagging and labeling the orders takes $20$ seconds, and then walking the bag to the pick$-$up area takes the bagger an additional $40$ seconds.

a$.(10$ points$)$ What is the capacity of the Tommy's Taco Shop $($in jobs per hour$)?$

b$.(10$ points$)$ Typically, $55$ customers arrive at Tommy's Tacos per hour. What is the utilization of the assemblers?