Individual Quantitative Literacy Case Study Report and Analysis

This report provides a quantitative analysis of a business case study involving a car wash and a kebab van, applying the Fermi problem methodology. The analysis includes calculating maximum gross revenue under different operational scenarios, considering factors like employee breaks, operational efficiency, and customer volume. The report presents detailed calculations, tables, and graphical representations to illustrate the financial outcomes of various business decisions. It also explores the potential profitability of a coffee shop associated with the car wash. The student demonstrates the ability to create numeric datasets, interpret them, and build a synthetic model to assess the financial performance of each business, ultimately drawing conclusions about their respective profit potentials.

Running Head: INDIVIDUAL QUANTITATIVE LITERACY
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Individual Quantitative Literacy Case Study
Name
Institution
Date

INDIVIDUAL QUANTITATIVE LITERACY 2
Individual Quantitative Literacy: Case Study
Queries pertaining mathematics, physics, and engineering need a lot of evaluations,
analysis, and calculations. In most instances, there are queries that do not have distinctive figures
and numerical to allow for the processes of evaluation, calculation, or analysis (Cheuk et al.,
2016). These are the cases where estimation comes in. estimation comes in the instances where
there is need to solve impossible queries or the difficult ones that most of the times carry the
infinite aspects. These are what we call as the Fermi queries and may include problems involving
populations, molecules, and many other aspects (Moore, 2016). The answers to these questions
are therefore analyzed and calculated through estimation to give a margin that represents the
correct answer (Prince & Simpson, 2016). The significance associate with these queries is that
they help students think critically, evaluate their understanding, and also interpret most of the
difficult situations they come across.
Task 1
Working hours 8 hours
Number of employees 12
Charges $40 for hand washing $10 for
vacuumed washing
Time 20 minutes for hand washing
10 minutes for vacuumed washing
The above case represents a businessman with two businesses. Just like in estimation
process, most of the calculations that can be analyzed from this case are based on assumptions
and numerical estimations.

INDIVIDUAL QUANTITATIVE LITERACY 3
Maximum gross revenue of the business operating all bays continuously in a 48 hour
period
From the information it is clear that the car wash has a total of four hand wash bays while
the vacuum bays are two. The case assumes that the operation that we are working with will take
48 hours. With 48 hours, it means that these are 2880 minutes of working given that the workers
work continuously. The employees are divided into two people for each bay for the sake of these
tasks. For each hand wash, a car will be serviced in ten minutes which also shows that in the
given minutes, each of the business hand bay will service 144 cars. Since the businessman has 4
bays, there will be a total of 1152 cars serviced due to the presence of two employees at each
bay.
In the vacuum bay, a car is serviced for ten minutes. In the operating 48 hours, it means
that 1152 cars will be done. When it comes to the charges, the businessman has placed a tag of
$40 for each car. This means that in the 48 hours, he will get revenue of $46080 when we work
with 1152 hours. When we get to the vacuum, $10 is charged for a car which means it will total
to $11520. This totally gives gross revenue of $57600.
Maximum gross revenue of the business operating with employee breaks included and all
bays active only 75% of the 48 hour period
When the bays operate at 75% efficiency rather than 100%, it means that they will be
working for 36 hours. On the same note, we are told that each employee gets a break of 1 hour in
every 8 hours. They then get 4 hours rest time which we are going to assume that they get after
the 8 hours. What this means is that each employee gets to work for 32 hours. This gives a total
of 1920 minutes. In this case, each bay service 96 cars in the hand wash while in the vacuum,
192 are done. This represents the number for each employee. For the 12 employees, two of them

INDIVIDUAL QUANTITATIVE LITERACY 4
will work per bay. This means that in the hand wash, 192 cars will be done while in the vacuum,
384 will be done. This then gives revenue of $7680 for the hand wash and $3840 for the vacuum.
In total, this is gross revenue of $11520.
working 48hrs Emp bks
0
10000
20000
30000
40000
50000
60000
70000
Fig.1: a graph showing the difference in gross revenue in each case.
Task 2
Operating time 12 noon to 12 pm.
Working hours 8 hours with a I hour break
Production rate 1 kebab in very 5minutes ( 6 can be
produced simultaneously)
charges $10 per kebab
Maximum gross revenue for the kebab van in every 98 hour period

INDIVIDUAL QUANTITATIVE LITERACY 5
To answer this, we need to assume that the work is done non-stop such that when one
employee breaks, the other takes over. One kebab is produced in 5 minutes. In 98 hours, 1176
kebabs will be made. 6 kebabs can however be made at the same time which means that in 98
hours a total of 7056 kebabs will be made. A kebab goes for $10. The 7056 kebabs will therefore
total to $70560. Since 4 employees are deployed at each van, the gross revenue will accumulate
to $2828240.
Maximum gross revenue for the kebab van in every 98 hour period inclusive of employee
breaks
During the 98 hours, employees break for 1 hour in every 8 hours. This means that they
will be working for 86 hours. In the 86 hours, they will make a total of 1032 kebabs. Given that
the vans make 6 kebabs at a go, 6192 kebabs will be made in the 86 hours. On the same note, we
have been told that there are four employees at each point or van which means that they will be
able to make 24768 kebabs. One kebab is $10 so the total revenue is $2474768.
Maximum gross revenue for the kebab van in every 98 hour period inclusive of employee
breaks operating at 75% efficiency
If the employees were to work without been given a break, they would be able to make
24768 kebabs within the 98 hours. When we assume that they are working on an efficiency of
100% rather than this 75%, 6 kebabs are made. At 75% only 4.5 are made. This means that they
make 18576 kebabs. At $10 each, they will make a total of $185760.

INDIVIDUAL QUANTITATIVE LITERACY 6
98hrs without break 98 hours with break working at 75%
eficiency Category 4
0
50000
100000
150000
200000
250000
300000
Fig.2: a graph showing the difference in gross revenue in each case.
Task 3
Sitting capacity 16
Number of customers 60% of the car wash customers
charges $4.50
Cost 30 cents
Working time 8 hours with a 1 hour break
To make money at the coffee shop, the owner must depend on the customers bringing
their cars for servicing. Estimates show that there are total of 2300 customers who can be served
by the car hand wash which means it is a possible market. Analysis from the case study reveals
that 60% of the customers visit the coffee shop. This means 1382 of them will be expected to
visit. At $4.50 a cup, it means that the coffee shop will make around $6219. The coffee
production costs stand at 30 cents per cup. This means that they will make a profit of $5804 after

INDIVIDUAL QUANTITATIVE LITERACY 7
deducting all the costs. With this information, I think a coffee shop would be the best idea since
it provides a customer base of 60% the one associated with the car wash.
Conclusion
From our analysis and calculations, each business in this case can be attached to a
specific gross profit. This means they are profitable and one can select any choice and make it a
big earn. From the analysis and assumptions made we can also see that one business can generate
different income from the other. With accurate consideration of Fermi queries which can directly
be linked to our case here, this task has made us reason to an estimated platform which has made
us come to such conclusions and figure.