Quantitative Analytics: Fermi Problems and Business Feasibility

This assignment, focusing on quantitative analytics and Fermi problems, analyzes the feasibility and profitability of business ventures. The student evaluates a car wash and a potential coffee shop, assessing revenue, profit margins, and operational efficiency. Task 1 examines hand wash and vacuum bays, calculating maximum gross revenue under different operational scenarios. Task 2 analyzes a kebab business, determining potential revenue based on varying operational hours and employee efficiency. Task 3 combines the car wash and coffee shop, estimating coffee shop customer numbers and calculating profit. The assignment uses assumptions and calculations to determine whether the coffee shop is a worthwhile investment. The conclusion highlights the use of quantitative analytics in business decision-making and the importance of considering startup capital and payback periods. The analysis is supported by the use of mathematical and statistical models.

Fermi Problems Quantitative Analytics 1
FERMI PROBLEMS QUANTITATIVE ANALYTICS
By (Name)
The Name of the Class (Course)
Professor (Tutor)
The Name of the School (University)
The City and State where it is located
The Date

Fermi Problems Quantitative Analytics 2
Fermi Problems Quantitative Analytics
Introduction
Quantitative analytics are normally used in business for problem-solving and strategic planning
purposes. Quantitative analytics refer to the assessment of business data through mathematical
and statistical models, tables, and visual charts designed to communicate critical information
about the business. The questions in this assignment will be taken as Fermi problems. As such,
Fermi problems will center on the determination of whether given attributes in approximation
and estimation of complex mathematical questions are satisfied (Ärlebäck & Bergsten, 2010).
We will analysis the performance of each of the businesses to see which one is the most feasible
and profitable based on maximum gross revenue. There is a need to see whether it is a good idea
for the car wash owner to open a coffee shop. If the revenues exceed the cost substantially then
the coffee shop will generate profit margins that will make the pursuit of the business venture
worthwhile.
TASK 1
Assumptions
1. The hand wash bays and vacuum bays operate independently i.e. a person can get his/her
washed without getting it vacuumed.
2. All bays have two employees each
3. There is no waiting time between one car and the next
Part I

Fermi Problems Quantitative Analytics 3
Calculations for the Four Hand wash bay
Hand Wash Bay 1 Bay 2 Bay 3 Bay 4
Hours Worked 48 48 48 48
Employees 2 2 2 2
Price Per Wash $40 $40 $40 $40
Each hand wash bay will attend to cars for 48 hours
If one car takes 20 minutes to wash
How many cars will be washed in 48 hours?
48∗60
20 =144 cars
One hand wash bay will cater to 144 cars
Four hand wash bay will cater to 144 multiplied by 4 = 576 cars
144
144144
144
Cars Washed
Bay 1 Bay 2 Bay 3 Bay 4

Fermi Problems Quantitative Analytics 4
If one car is hand washed for $40
How much will it get for hand washing 576 cars?
576∗40=$ 23,040
Calculations for the two vacuum bays
Hand Wash Bay 1 Bay 2
Hours Worked 48 48
Employees 2 2
Price Per Wash $10 $10
Each vacuum bay will attend to cars for 48 hours
If one car takes 10 minutes to vacuum
How many cars will be vacuumed in 48 hours?
48∗60
10 =288 cars
One vacuum bay will cater to 288 cars
Two vacuum bays will cater to 288 multiplied by 2 = 576 cars

Fermi Problems Quantitative Analytics 5
288288
Cars Washed
Bay 1 Bay 2
If one car is hand washed for $10
How much will it get for hand washing 576 cars?
576∗$ 10=$ 5,760
Maximum Gross Revenue
$ 23,040+$ 5,760=$ 28,800
PART II
Calculations for the Four Hand wash bay
If the bays will be available for 75% of the 48 hours,
For how long will the bays be operational?
75∗48
100 =36 h ours
Hand Wash Bay 1 Bay 2 Bay 3 Bay 4

Fermi Problems Quantitative Analytics 6
Hours Worked 36 36 36 36
Employees 2 2 2 2
Price Per Wash $40 $40 $40 $40
Hence each hand wash bay will attend to cars for 36 hours
Each worker works 7hours in every 8 hours (1 hour break)
How many hours will each employee work in 36 hours?
7∗36
8 =31.5(we will round up)=32 h ours
If one car takes 20 minutes to wash
How many cars will be washed in 32 hours?
32∗60
20 =96 cars
One hand wash bay will cater to 96 cars
Four hand wash bay will cater to 96 multiplied by 4 = 382 cars
If one car is hand washed for $40

Fermi Problems Quantitative Analytics 7
Bay 1 Bay 2 Bay 3 Bay 4
$0
$500
$1,000
$1,500
$2,000
$2,500
$3,000
$3,500
$4,000
$4,500
Revenue
Revenue
How much will it get for hand washing 382 cars?
382∗$ 40=$ 15,280
Calculations for the two vacuum bays
If the bays will be available for 75% of the 48 hours,
For how long will the bays be operational?
75∗48
100 =36 h ours
Hand Wash Bay 1 Bay 2
Hours Worked 36 36
Employees 2 2
Price Per Wash $10 $10
Each vacuum bay will attend to cars for 36 hours

Fermi Problems Quantitative Analytics 8
Each worker works 7hours in every 8 hours (1 hour break)
How many hours will each employee work in 36 hours?
7∗36
8 =31.5=32 h ours
If one car takes 10 minutes to vacuum
How many cars will be vacuumed in 32 hours?
32∗60
10 =192 cars
One vacuum bay will cater to 192 cars
Two vacuum bays will cater to 192 multiplied by 2 = 384 cars
If one car is hand washed for $10
Bay 1 Bay 2
$0
$500
$1,000
$1,500
$2,000
$2,500
Revenue
Revenue
How much will it get for hand washing 384 cars?

Fermi Problems Quantitative Analytics 9
384∗$ 10=$ 3,84 0
Maximum Gross Revenue
$ 15,280+$ 3,840=$ 19,120
TASK 2
Assumptions
1. One day is a 24 hour period
2. The business runs for 14 hours each day
3. There is no waiting time between one car and the next
Part I
If the business runs for 14 hours every 24 hour period
How long will it run for every 98 hour period?
14∗98
24 =57.17∨57 h ours
If six kebabs are produced in 5 minutes
How many will be produced in 57 hours?
6∗57∗60
5 =4104 kebabs
One kebab is $10

Fermi Problems Quantitative Analytics 10
How much will 4104 kebab bring in?
Maximum Gross Revenue
4104∗$ 10=$ 41,040
Part II
If the business runs for 14 hours every 24 hour period
How long will it run for every 98 hour period?
14∗98
24 =57.17∨57 h ours
Each worker works 7hours in every 8 hours (1 hour break)
How many hours will each employee work in 57 hours?
7∗57
8 =49.8=50 h ours
If six kebabs are produced in 5 minutes
How many will be produced in 50 hours?
6∗50∗60
5 =3600 kebabs
One kebab is $10
How much will 3600 kebab bring in?
Maximum Gross Revenue

Fermi Problems Quantitative Analytics 11
3600∗$ 10=$ 36,000
Part III
If the business runs for 14 hours every 24 hour period
How long will it run for every 98 hour period?
14∗98
24 =57.17∨57 h ours
Each worker works 7hours in every 8 hours (1 hour break)
How many hours will each employee work in 57 hours?
7∗57
8 =49.8=50 h ours
If they work at 75% efficiency
75∗50
100 =37.5 h ours
If six kebabs are produced in 5 minutes
How many will be produced in37.5 hours?
6∗37.5∗60
5 =2700 kebabs
One kebab is $10
How much will 2700 kebab bring in?
Maximum Gross Revenue

Fermi Problems Quantitative Analytics 12
3600∗$ 10=$ 27,000
TASK 3
Assumption
1. Out of the 60% of car wash clients; each car accounts for only one coffee shop customer
2. The hand wash bays and vacuum bays operate independently i.e. a person can get his/her
washed without getting it vacuumed.
3. They work continuously across the 48 hour period
Assessment
In the 48 hours the employers will have 6 breaks i.e. 48/8=6
Each break lasts hour each hence the breaks will total 6 hours i.e. 6 breaks*1 hour=6 hours
Total work hours less break hours to get the productive time i.e. 48-6=42
In 42 hours (affect subtracting employee breaks) the number of customers to the coffee shop
from the car wash are:
Four Hand Wash Bays
If one car takes 20 minutes to hand wash
How many cars will be washed in 42 hours across all four hand wash bays?
42∗60∗4
20 =504 cars