Q$3\mathrm{.}8($Algo$)$ Starbucks $[3\mathrm{.}6]$

After an "all night" study session the day before thelr last final exam, four students decide to stop for some much$-$needed coffee at the

campus Starbucks. They arrlve at $8$:$30$ a$.$m$.$ and are dismayed to find a rather long line.

Fortunately for the students, a Starbucks executlve happens to be In IIne 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 cashler 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 cashler'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 two

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 one

minute of work of the espresso drink maker.

Ground coffee customers buy one of Starbucks' many varletles of whole bean coffee and have it ground to thelr

specification at the store. This requires a total of one minute of the cashler's tlme $(20$ seconds to pour the coffee and $40$

seconds to grind the whole bean coffee$).$

The customers arrlve unlformly at the following rates from $7a.m.($when the store opens$)$ untl $10a.m.($when the morning

rush Is over$),$ with no customers arrlving after $10a.m$ :

III. Arrlval Rates:

Drlp coffee customers: $24$ per hour.

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

Espresso drink customers: $71$ per hour.

Ground coffee customers: $5$ per hour.

IV$.$ Each customer spends, on average, $19$ seconds with the cashler to order and pay. Approximately $23$ percent of all customers

order food, which requires an additional $20$ seconds of the cashler's time per transaction.

While walting in Ine, the students reflect on these facts and they answer the following questions:

a$.$ What is the implied utilization of the frozen drink maker? $($Do not round intermediate calculations. Round the answer to $2$ decimal

places.$)$

Answer is complete and correct.

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

Answer is complete and correct.

From thelr conversation with the executlve, the students learn that Starbucks is considering a promotion on all scones $($half pricel$),$

which marketling surveys predict will increase the percentage of customers ordering food to $25$ percent $($the overall arrlval rates of

customers wll not change$).$

c$.$ What wlll be the new implied utilization for the cashier if this promotion is implemented? $($Do not round intermediate calculations.

Round the answer to $2$ decimal places.$)$

Answer $?$