Business Analytics: Mathematical Model, Costing, and Advertisement Impact

This report explores the use of mathematical models in business analytics, including profit and loss calculations and five-year projections. It also discusses costing and revenue behavior, as well as the impact of advertisement expenditure on sales. Various marketing strategies, such as social media marketing and email marketing, are also discussed.

Business analytics
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Table of content
Introduction......................................................................................................................................3
Mathematical model....................................................................................................................3
Correlation –coefficient of advertising and sales........................................................................8
Internal revenue service in UK..................................................................................................13
Conclusion.....................................................................................................................................16
References......................................................................................................................................18
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Introduction
Business analytics is a continuous process in which business uses statistical data to gain
insight about the Strategies and also with the help of statistical data and techniques business try
to improve their decision making process (Vidgen and et.al 2017). This report includes
mathematical model and also provides profit and loss for the company by using mathematical
model. Apart from this costing and revenue behaviour is being defined in this report. In this
report correlation Coefficient between advertising and sale for the company is being mentioned.
Is report also shows the impact of advertising expenditures on sales and marketing of the
company so that company can gain competitive advantage. Apart from this statistical data about
GDP and Employment is being mentioned in this report.
Mathematical model
Particular Amount
Annual output 180000 units
Fixed cost 60,000
Variable cost 0.75
Sales price 2.00
(i) Mathematical model
Y= a+bx
=60000+0.75*180000
=195000
(ii) Profit and loss
(Sales price * 180000) – (variable cost*180000)
= (2.00*180000) – (0.75*180000)
=360000-135000
=225000 will be the profit of the company
(iii) Five year projection
For January 2022
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Particular Amount
Annual output 189000 units
Fixed cost 60000
Variable cost 0.81
Sales price 2.00
Y= a+bx
60000+0.81*189000
213090
For January 2023
Particular Amount
Annual output 198450 units
Fixed cost 60000
Variable cost 0.87
Sales price 2.00
Y= a+bx
60000+0.87*198450
232651.5
For January 2024
Particular Amount
Annual output 208372.5 units
Fixed cost 60000
Variable cost 0.93
Sales price 2.00
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Y= a+bx
60000+ 0.93*208372.5
2557896.80
For January 2025
Particular Amount
Annual output 218791.12 units
Fixed cost 60000
Variable cost 1.00
Sales price 2.00
Y= a+bx
60000+1.00*218791.12
278791.12
For January 2026
Particular Amount
Annual output 236294.4 units
Fixed cost 60000
Variable cost 1.08
Sales price 2.00
Y= a+bx
60000+1.08*236294.4
308109.12
Mathematical model represents the movement and behaviour of real objects older result and
outcomes of such objects will be defined and mathematical language (Appelbaum and et.al
2017). Mathematical language includes algebraic equation differential equation integral equation
theorems and algorithm.
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The main motive of using mathematical model by the company is to decrease the extra
cost and also company wants to save their valuable time. Financial modelling is being used to
know the exact profit and loss faced by the company why not putting so much capital. Apart
from this the process of mathematical model is easy and do not consume more time. Another
reason of using mathematical model is to analyse the sales revenue fixed cost and output of the
company so that if they found any error or difficulty and generating profit they can analyse the
whole values and can make certain corrections so that company do not have to face loss. Apart
from this mathematical model helps the company to make predictions for the future.
This will help the company to know how much products they have to generate in the
future by seeing the market Trends and customer demand so that did not produce so much
products that it will become difficult for the company to sell all the products so as per the market
demand with the help of mathematical modelling the can make predictions about the future
supply (Pappas and et.al 201). So mathematical model provides Real world scenario and
phenomena to the company and as per the given information managers of the company can make
different Strategies and policies for the future. To generate high profit it is mandatory for the
company that this specified that object then only mathematical model can then read them better
results otherwise company mein face loss if they do not know their objective in this case
mathematical model will not work appropriately.
Apart from objective company has to keep an eye on the variables and parameters
because mathematical model Fox on some assumptions. As per the assumptions company can
know who whom they want to target what age group people will use the products how much they
will sell the products what will be the quantity of the products etc. has been defined in
assumptions. As per the assumptions company produces new products and fulfil the demand of
the market.
Costing and revenue behaviour
To evaluate the performance of the business every company has to make sure about the cost and
the behaviour of revenue (Ashrafi and et.al 2019). Then only company can get to know whether
they are in profit or loss. If the cost of the company is higher than the revenue it shows that
company is in loss.
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Cost of the company can be categorised into two forms first is variable cost and other is
fixed cost. In this case fixed cost is 60000 which remains fixed for the entire life of the cost and
other cost is variable which varies from time to time. Is per the data it has been found that when
the output it increased by 5% the coast also increased by 8% but company is in profit because
their when us higher than their cost.
Profit is the difference between revenue and cost. So every company wants that, their
coast remains lower than their revenues. But to generate high revenue it is the responsibility of
the company that produce higher quality product for that they need to put more money in their
cost like to buy raw material for rent extra charges have to be paid by the company then only
they can deliver high quality product (Shah and et.al 2020. On the flip side company wants to
cut down its cost as well for that company needs to make proper budget and they have to
estimate and forecast the cost so that they can save the extra and unnecessary expenses.
As the company can’t make changes in the fixed cost but they can cut down variable
cost. According to the given data when the company was increasing the variable cost its output
also getting increased the reason behind is that when company is putting more amount in
variable cost it can produce more high quality products which is liked by the customers that’s
why their annual output in sales got increased.
As customer wants new and quality products and when they get the quality products they
do not feel hesitated in pain higher amount for the product this is the reason of increased revenue
and sales for the company. Therefore their annual output is continuously increasing due to the
increase in variable cost (Samui and et.al 2020). Another reason for increase in output is that
companies expanding more money on promotion and marketing activities so that company can
tap into new markets as well and try to touch all the customers who are not aware with the
products of the company. Apart from this company is trying to increase their revenue by offering
quality products to the customers for that they have to purchase high priced raw materials this is
also another reason that their variable cost is continuously increasing along with their revenue.
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year 2022 year 2023 year 2024 year 2025 year 2026
0
50000
100000
150000
200000
250000
Correlation –coefficient of advertising and sales
YEAR Advertising expenditure (X)
(£000s)
Sales revenue (Y)
(£000s)
2016 2 60
2017 5 90
2018 4 70
2019 6 100
2020 3 80
X-Mx Y-My (X-Mx)2 (Y-My)2 (X-Mx)(Y-
My)
-2.000 -20.000 4.000 400.000 40.000
1.000 10.000 1.000 100.000 10.000
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0 -10.000 0.000 100.000 0.000
2.000 20.000 4.000 400.000 40.000
-1.000 0.000 1.000 0.000 0.000
4.000 80.000 10.000 1000.000 90.000
Calculation
Values of X
∑=20
Mean=4
∑(X-Mx)2 =SSx =10
Values
Y
∑=40
Mean=80
∑(Y-My)2 =SSy =1000
XandY
Combined
N =5
∑(X-Mx)(Y-My)=90
Calculation
r=∑((X-My)(Y-Mx))/√((SSx)(SSy))
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r=90/√((10)(1000))=0.9
1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5
0
20
40
60
80
100
120
Y-Values
The above calculation shows that there is a strong and a positive correlation is present between
both the variables, which represents high X variable will go with high Y variable. It means I
advertisement experience will generate high sales revenue for the company (Skrypnikov and et.al
2017).
Impact of advertisement expenditure on sales
Is advertisement is one of the important part of any company with the help of advertisement
company can promote its products and services to others and specially its targeted customers.
From the above data it can be e said that marketing manager of this company is making correct
Strategies for advertisement as the correlation between both the variables shows that when the
expenses on expenditure is increases it directly impact the sales and revenue of the company.
Advertisement have both long term and short term impact on the sales revenue of the company
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but it depends on the objective and goal of the company what kind of advertisement they should
prefer (Sepehri, A., 2017).If the company is doing short term advertisement it will definitely
going to impact the sales and revenue of the company but the time duration of such increased
sales will be shorten. But on the other hand when the company wants to earn the competitive
edge in the market it would be preferred that they should go for long term in advertisement.
For long-term advertisement the cost and expenditure will be higher as compared to short
term advertisement. Expert about table in data it can be said that company is having good
revenue and sales it means the demand of the product is higher in the market. If the product of
the company is being demanded in the market this can only becomes possible with the proper
advertisement and promotional activities.
As the marketing manager of the company is highly concerned for advertisement so that
it can increase the brand awareness about the company in the market (Kinchin and et.al
2017).With the help of advertisement more and more people will come to know about the
features of the products. This will help the company to know whom they should target and what
the preference of the customers is.
It has been seen from the correlation of Coefficient is that company should increase the
expenditure on advertisement because when we will put more money in advertisement so the sale
of the company will automatically increase (Assimakopoulos and et.al 2017).
The main motive of Marketing department behind the increased advertisement is that
they want to bring together its customers and the products of the. But the marketing manager has
to be sure that the do not spend ample of money on advertisement so that they may face loss
(Strauss and et.al 2018)). As marketing and advertisement is important for the company but they
do not compromise with their profit.
To gain the competitive advantage this company should do more advanced and modern
advertisement. For that they are some marketing strategies which can be implemented by the
marketing managers to increase the revenue and sales of the company.
Social media marketing
Now a day’s every people have their account on social media and thousands of people are
active user of social media. Show the marketing department of the company can share various
contents images videos and pictures of the product on their social media handle so that by
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sharing a single image taken tab 2007 billions of customer who are actively using social media
(Samiee and et.al 2019). Along with this company can know the current market Trend and
decides of the customer so that they can produce different and innovative product to increase
their loyal customer.
Internet marketing
This kind of marketing company can update its website and show the latest of words and
products which is being sold by the company. Because the trend has been changed, now
customers prefer to buy products online (Goncharova and et.al 2019). To increase the sale
company can tie up with any E-Commerce company to increase their sales apart from this
weekend sale the products directly to the customer with the help of their website. But to sell
products online company must provide all the necessary details about the product like quantity
price images quality etc. So that customer can make right choice.
Email marketing
This is one of the popular marketing strategies which are being followed by most of the
companies to increase their sales (Arafah, W., 2018). Indus marketing company uses the old data
of its customers and send those emails on monthly or weekly basis so that they’ll customer can
get to know what the different offers are and discounts are being provided by the company.
Updating of content
To increase the sales it is necessary for the company that they must update their contents,
whenever they make any changes (Kingsnorth, 2019). To increase the sale it is must, for the
company that they do not publish old content on their website it will reduce the reputation of the
company in the market. Show the marketing manager has to make sure that what kind of latest
products they are about to offer to its customers so they on the publish such information on the
website and social media otherwise it may lose loyal customer because every customer wants
different products they don’t want to use similar products all the day so to increase the market
share and to survive in the market it is necessary for the company that day continue update the
information about their products.
Price
Price is effective marketing strategy which is definitely going to work for the company. If
the company e makes any change in the price or reduced the price it will definitely draw the
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attention of customers, and Company can gain competitive advantage as well and give a tough
competition to its competitors.
Target market and audience
If the company wants to increase its competitive edge in the market so it is very necessary
for them to know in which market they want to sell their products and what are their target
audience. This can only be known by advertising (Mothersbaugh, and et.al 2019) When the
company know its target market they can easily sell its products to the customer. To choose the
correct target market company need to do research in the market so that they can know the
perspective of customers and also their buying behaviour.
Internal revenue service in UK
Internal revenue service in UK refers to the collection of tax and administering revenue.
All these revenues are being collected by the government of UK so that they can use such
amount for the development of the country and also they can provide better services for the well-
being and development of society and people of UK.
a (i) The two economic variables are GDP and employment.
Growth of GDP provides and Inverse relation with employment (Morgan and et.al 2019). It has
been seen that if a country is having highest employment but there are chances that that GDP do
not increase because GDP and employment has inverse relationship. As GDP stands for gross
domestic product, which shows the final monetary value of those products which have been
manufactured and produced within the country. The time duration of such products are also
specified usually one year is consider. In short GDP is used to economy of a country for a year.
Growth of GDP shows that how fast the economy of a country is going (Amelia and et.al 2019).
On the other hand employment shows that how many people are having paid jobs in their hands.
Basically employment it is a contract or agreement between employer and employee that
employee will provide services to the company in result company will provide them wages and
salary so that they can fulfil their needs.
As the GDP of UK is concerned with producing new products in the country so there is a
high possibility of employment as well because when more and more companies will open in UK
so the goods and products will be produced and delivered more does they will need more labours
so there is a high chance that more and more labour will get employment but it can be permanent
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basis or temporary basis so if the economy of a country and GDP of a country is going higher it
doesn’t mean that all the unemployed people will get employment. Government of UK is trying
to provide employment to all the people but it is very difficult to give jobs and opportunities to
all the people of UK (Li, F and et.al 2021). Therefore government can’t spend too much amount
for the development and welfare of unemployed people as if they have skills and qualification
they may easily get some employment opportunities or they can run their own start-ups and
business in UK.
So in UK GDP can rice and can grow with or without higher employment. But it has
been found that when the employment of the country is in strong position that its GDP will
automatically rise but when inflation comes even though the GDP of UK has survived and do not
get decreased. In the current scenario the GDP of UK is falling down due to the dynamic as the
debt of the country has increased and people do not have employment and necessary work to do.
So the entire economic sector of UK has been impacted from the crisis. The main reason behind
falling in GDP of UK is that there is a continuous downfall in energy sector of UK hotel and
Catering sector of UK all the banking sector the entire Financial Institutions are running short of
funds this has impacted the entire growth of UKs economy.
(ii) Spurious correlation
Spurious correlation shows the relation between two variables both are casual in nature but they
are not (Key and et.al 2017. The presences of casual relationship between two variables take
place because of similar movements. The relation between employments in GDP is one of the
examples of superior correlation as in that, both the variables track down each other very and
also their values get affected by many factors.
If any factor impact the GDP of UK it will directly impact the employment as well so
what the variables have casual relationship but they are not show related to each other. Show the
movement in GDP whether it is going high or falling down this will definitely going to affect the
employment of the country.
Cross sectional data
Cross-sectional data refers to the analysis of any data set for a specified time duration.
The very common example of cross sectional government records and also the survey which is
being conducted by the government can be used as an example of cross sectional data
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From the above data of GDP growth of UK shows that UK has faced use downturn in the
economy in 2009. In the year 2009 Gross Domestic Product of UK fall down by 4.25% due to
the financial crisis.
But the GDP of UK survived and increased in 2010 by 1.95 percent but in 2011 again UK
has to face some downfall in GDP and the rate of GDP decreased by 0.41 % similarly in 2012
GDP was not recovered and in 2013 the growth of GDP has changed to 2.14 % which is higher
than 2011. From 2013 to 2015 the UK economy was doing well but in 2016 again GDP has to
face downturn and it reduced by 0.25% and continuously the GBP of UK is going down. In 2019
the GDP was started recovering but again the pandemic hit it the GDP of UK badly and again
this country as facing huge loss.
As per the above data it has been seen that from 2009 to 2011 the employment rate of UK
I was continuously increasing but from 2012 to 2019 the government is trying to provide
employment to all the people those who have qualification and skills but the unemployment rate
of UK as not going to decrease anymore but from 2012 to 2019 government has tried to reduce
the unemployment rate and government becomes successful in providing employment
opportunities to most of the people.
Correlation of Coefficient shows the relationship between two variables. The main
objective of calculating correlation of Coefficient is to measure how strong the relationship
between two variables (U.K. Unemployment Rate, 2020). Correlation is used as a linear
regression. If the correlation shows positive or negative change in one variable will affect the
change in another variable as well. If the correlation of Coefficient is less than one it shows that
any positive increase in one variable will impact negative or less on other variable. If the
coefficient of correlation is zero it shows that every positive impact on any variable will not
affect another variable. The major advantage of calculating correlation of Coefficient is to
analyse the relationship between both the variables and how both the variables will get change or
remain same if one variable get affected by any factor.
GDP growth of UK
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Year Growth in GDP
(%)
Changes
(Annually)
2019 1.46% 0.12%
2018 1.34% -0.55%
2017 1.89% -0.03%
2016 1.92% -0.44%
2015 2.36% -0.25%
2014 2.61% 0.47%
2013 2.14% 0.66%
2012 1.48% -0.06%
2011 1.54% -0.41%
2010 1.95% 6.20%
2009 -4.25% -3.97%
UK unemployment rate
Year Unemployment
rate
Change on
annual basis
2019 3.85% -0.15%
2018 4.00% -0.34%
2017 4.34% -0.48%
2016 4.81% -0.49%
2015 5.30% -0.81%
2014 6.11% -1.42%
2013 7.53% -0.36%
2012 7.89% -0.15%
2011 8.04% 0.25%
2010 7.79% 0.25%
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Conclusion
After analysing the entire report it can be concluded that this report States about business
analytic. This report contains mathematical model and how company can use mathematical
model to evaluate its cost and profit. Besides this by using mathematical model how
communication earn profit or loss is been mentioned in this report. This report contains five year
projection through which company can realise how much profit or loss they are about to gain in
the coming years. Cost and revenue behaviour is also mentioned in this report. This report also
speaks about the correlation Coefficient between advertisement and sales. Apart from this how
advertisement and expenditure on promotional activities impact the sale of the company as
mentioned in this report. This report also defines relevant marketing strategies for the company.
Internal revenue service’s is being defined in this report this report also shows some statistical
data of GDP and employment.
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References
Books and Journal
Vidgen and et.al 2017. Management challenges in creating value from business
analytics. European Journal of Operational Research.261(2). pp.626-639.
Appelbaum and et.al 2017. Impact of business analytics and enterprise systems on managerial
accounting. International Journal of Accounting Information Systems.25.pp.29-44.
Pappas and et.al 2018. Big data and business analytics ecosystems: paving the way towards
digital transformation and sustainable societies.
Ashrafi and et.al 2019. The role of business analytics capabilities in bolstering firms’ agility and
performance. International Journal of Information Management. 47. pp.1-15.
Shah and et.al 2020. Qualitative analysis of a mathematical model in the time of COVID-
19. BioMed Research International, 2020.
Samui and et.al 2020. A mathematical model for COVID-19 transmission dynamics with a case
study of India. Chaos, Solitons & Fractals.140.p.110173.
Skrypnikov and et.al 2017. Mathematical model of statistical identification of car transport
informational provision. ARPN Journal of Engineering and Applied Sciences.12(2).
p.511.
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Sepehri, A., 2017. A mathematical model for DNA. International Journal of Geometric Methods
in Modern Physics.14(11). p.1750152.
Kinchin, I. and Doran, C.M., 2017. The economic cost of suicide and non-fatal suicide behavior
in the Australian workforce and the potential impact of a workplace suicide prevention
strategy. International journal of environmental research and public
health. 14(4).p.347.
Strauss and et.al A review of choice-based revenue management: Theory and
methods. European Journal of Operational Research. 271(2). pp.375-387.
Mothersbaugh, and et.al 2019. Consumer behavior: Building marketing strategy. McGraw-Hill
Higher Education.
Morgan and et.al 2019. Research in marketing strategy. Journal of the Academy of Marketing
Science. 47(1).pp.4-29.
Li, F and et.al 2021. Social media marketing strategy: definition, conceptualization, taxonomy,
validation, and future agenda. Journal of the Academy of Marketing
Science. 49(1).pp.51-70.
Key and et.al 2017. Upstream social marketing strategy: An integrated marketing
communications approach. Business Horizons. 60(3). pp.325-333.
Amelia and et.al 2019. Effect of Marketing Strategy and Service Quality Against the Decisions
of Parents. Ilomata International Journal of Management.1(1).pp.31-37.
Assimakopoulos and et.al 2017. Effective social media marketing strategy: Facebook as an
opportunity for universities. International Journal of Retail & Distribution
Management.
Samiee, S. and Chirapanda, S., 2019. International marketing strategy in emerging-market
exporting firms. Journal of International Marketing. 27(1).pp.20-37.
Goncharova and et.al 2019. Brand platform as an element of a company marketing
strategy. International Journal of Supply Chain Management. 8(4). p.815.
Arafah, W., 2018. Marketing strategy for renewable energy development in Indonesia context
today.
Kingsnorth, S., 2019. Digital marketing strategy: an integrated approach to online marketing.
Kogan Page Publishers.
Online
U.K. Unemployment Rate, 2020[online] Available through
<https://www.macrotrends.net/countries/GBR/united-kingdom/unemployment-rate>
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