Q$3\mathrm{.}8($Starbucks$)$ After an "all night" study session the day before their last final exam, four students decide to stop for some much$-$needed coffee at the campus Starbucks. They arrive at $8$:$30$ a$.$m$.$ and are dismayed to find a rather long line.

Fortunately for the students, a Starbucks executive happens to be in line directly in front of them. From her, they learn the following facts about this Starbucks location:

I. There are three employee types:

There is a single cashier who takes all orders, prepares nonbeverage food items, grinds coffee, and pours drip 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.

II$.$ 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 the 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 Starbucks' many varieties of whole bean coffee and have it ground to their specification 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$).$

III. The customers arrive uniformly at the following rates from $7a.m.($when opens$)$ until $10a.m.($when the morning rush is over$),$ with no customers anting $10$ a$.$m$.$:

Drip coffee customers: $25$ per hour.

Blended and iced drink customers: $20$ per hour.

Espresso drink customers: $70$ per hour.

Ground coffee customers: $5$ per hour.

IV$.$ Each customer spends, on average, $20$ seconds with the cashier to order and po$.$

V$.$ Approximately $25$ percent of all customers order food, which requires an ads $20$ seconds of the cashier's time per transaction.

While waiting in line, the students reflect on these facts and they answer the follo questions:

a$.$ What is the implied utilization of the frozen drink maker?

b$.$ Which resource has the highest implied utilization?

From their conversation with the executive, the students learn that Starbucks is sidering a promotion on all scones $($half price!$),$ which marketing surveys predin increase the percentage of customers ordering food to $30$ percent $($the overall arivid of customers will not change$).$ However, the executive is worried about how this affect the waiting times for customers.

c$.$ How do the levels of implied utilization change as a response to this promotion?