Show me the steps to solve :Problem $1$: Spiffy Car Wash

Spiffy Car Wash offers four types of service to its customers:

The Basics: simple car wash$/$dry

Deluxe Wash: wheels cleaned, then car wash$/$dry

Deluxe Wash and Wax: wheels cleaned, car wash$/$dry$,$ car waxed

The Works: wheels cleaned, car wash$/$dry$,$ car waxed, interior of the car detailed

Activity descriptions, times, and staffing are provided below for the various cleaning stations:

Station

Description

Number of Workers$/$Machines

Processing Time $($per car$)$

Wheel Cleaning

Manually clean all four wheels

$1$ dedicated worker

$5$ minutes

Car Wash$/$Dry

Automated cleaning and drying process

$1$ car wash machine with $1$ dedicated worker

$5$ minutes

Car Wax

Manually apply wax

$1$ dedicated worker

$30$ minutes

Interior Detailing

Manually clean and vacuum the interior of the car

$2$ dedicated workers

$60$ minutes

Assume that on average cars arrive uniformly at a rate of $10$ cars per hour during the hours of $8$:$00$ am and $6$:$00$ pm $($the hours in which Spiffy is open for business$).$ Also, $40\%$ of the customer's request the Basics, $30\%$ request the Deluxe Wash, $20\%$ request the Deluxe Wash and Wax, and $10\%$ request The Works.

$1.$

Question $1$

Which of the four stations is the bottleneck?

$1$ point

Car Wax

Interior Detailing

Car Wash $/$ Dry

Wheel Cleaning

$2.$

Question $2$

What is the implied utilization at the Interior Detailing station? Write your answer as an integer.

$1$ point

Enter answer here

Spiffy decides to offer a special holiday price through the month of December on its service $$The Basics$.$ As a result, the demand rate increases to $15$ cars per hour, uniformly distributed during the hours of operation. This special also results in a change in the mix of services demanded. Now, $70\%$ of customers request The Basics, $20\%$ request the Deluxe Wash, $5\%$ request the Deluxe Wash and Wax, and $5\%$ request The Works.

$3.$

Question $3$

How is the process performance of Spiffy affected?

$1$ point

There is a new bottleneck in the process.

The number of cars that may be processed per day at Spiffy increases.

The number of cars that may be processed per day at Spiffy decreases.

Both A and B

Both A and C