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:

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.

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 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$$ many varieties of whole bean coffee and have it ground to their specification at the store. This requires a total of one minute of the cashier$$s time $(20$ seconds to pour the coffee and $40$ seconds to grind the whole bean coffee$).$

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

Arrival Rates:

Drip coffee customers: $26$ per hour.

Blended and iced drink customers: $19$ per hour.

Espresso drink customers: $63$ per hour.

Ground coffee customers: $5$ per hour.

Each customer spends, on average, $21$ seconds with the cashier to order and pay. Approximately $26$ percent of all customers order food, which requires an additional $18$ seconds of the cashier$$s time per transaction.