Problem $3$These are some questions about operational management

After an all$-$night study session the day before their last final exam, four SWUFE students decide to

stop for some much$-$needed coffee at the campus coffee shop StarYuans. They arrive at $8$:$30$am and

are dismayed to find a rather long line. Fortunately for the students, a StarYuans executive happens

to be in line directly in front of them. From her, they learn the following facts about this StarYuans

location:

There are $3$ employee types:

There is a single cashier who takes all orders, prepares non$-$beverage food items, grinds coffee,

and pours drop coffee.

There is a single frozen drink maker who prepares blended and iced drinks.

There is a single espresso drink maker who prepares espressos, lattes, and steamed drinks.

There are typically four types of customers:

Drip coffee customers order only drip coffee. This requires $20$ seconds of the cashier's time to

pour the coffee.

Blended and iced drink customers order a drink that requires the use of a blender. These

drinks take on average $2$ minutes of work of the frozen drink maker.

Espresso drink customers order a beverage that uses espresso and$/$or steamed milk. On

average, these drinks require $1$ minute of work of the espresso drink maker.

Ground coffee customers buy one of StarYuans' many varieties of whole bean coffee and have

it ground to their specifications at the store. This requires a total of $1$ minute of the cashier's

time $(20$ seconds to pour the coffee and $40$ seconds to grind the whole bean coffee$).$

Customers arrive uniformly at the following rates from $7am$ when the store opens until $10$am when

the morning rush is over, with no customers arriving after $10$am:

Drip coffee customers: $\frac{25}{h}r,$

$>$ Blended and iced drink customers: $\frac{20}{h}r,$

$>$ Espresso drink customers: $\frac{70}{h}r,$

$>$ Ground coffee customers: $\frac{5}{h}r.$

Each customer spends on average $30$ seconds with the cashier to order and pay. About $25\%$ of

customers order food, which requires an additional $20$ seconds of the cashier's time. While waiting

in line, the students reflect on these facts and ask themselves:

What is the implied utilization of the frozen drink maker?

Which resource has the highest implied utilization?

From their conversations with the executive, they learn that StarYuans is considering a

promotion on scones, which will likely increase the percentage of customer ordering food to $30\%.$

How will this affect the implied utilization of the cashier? $($answer this as the new utilization$)$