Business Analytics: Mathematical Model and Correlation Analysis for Darko Farms Limited and Mansion Plc

This report provides a mathematical model for Darko Farms Limited (DF Ltd.), calculation of profit or loss, five-year projection, and correlation analysis for advertisement and revenue. It also includes a discussion on marketing expenses' impact on profitability and recommendations for gaining a competitive edge. The subject is Business Analytics and the course code is LUBM303.

Assignment Code: LUBM303
Student Name:
Student ID:
1

Table of Contents
Introduction......................................................................................................................................3
Question 1........................................................................................................................................3
a) The mathematical model for Darko farms limited (DF Ltd.)...............................................3
b) Calculation of the profit or loss of Darko farms limited (DF Ltd.)..................................4
c) Five-year projection of Darko farms limited (DF Ltd.)........................................................4
d) Darko farms limited (DF Ltd.) costs and revenues assessment plus commentary...........7
Question 02......................................................................................................................................8
1. Advertisement and revenues correlation analysis evaluation...............................................8
Comments....................................................................................................................................9
2. Advertisement expenditures and revenue income are depicted in a scatterplot...................9
The relationship between different elements is explored for both structures:...........................10
3. Impact spending and sales are the subjects of a deep inspection and suggestions.............10
Marketing expenses’ impact on profitability.............................................................................10
Question 03....................................................................................................................................12
a) Break-Even Point of Mansion Plc......................................................................................12
b) Evaluation discussion of Mansion Plc............................................................................14
c) Factors Mansion PLC’s management should consider before committing the company to
the course of action....................................................................................................................14
d) The study examines the benefits and downsides of employing the break-even concept:
14
Conclusion.....................................................................................................................................15
References......................................................................................................................................16
2

Introduction
According to Mikalef et al., (2020) “Business analytics is a set of disciplines and technologies
for solving business problems using data analysis, statistical models and other quantitative
methods which involves an iterative, methodical exploration of an organization’s data, with an
emphasis on statistical analysis, to drive decision-making.” This report analyzes four different
types of problems using business analysis methods. Four different problems are solved using
mathematical solutions. This report also provides those calculations.
Question 1
a) The mathematical model for Darko farms limited (DF Ltd.)
This arithmetical approach would be a functional interpretation structure that uses empirical
terms to explain overall functioning like any entity (Seddon et al., 2017). Computational
mathematics tools include complex architectures, inferential statistical methods, convergent
formulas, and random metaheuristic algorithms, among name just a handful. Humanity’s
fundamental simple mathematical estimations are also a more powerful human representation.
Consequently, practically anything within physical and sensory cosmos that can be properly
described via notions underpinning numerical formulae emerges available scientific quantitative
framework examination, whether organic or involving active stake and creation. The following is
just a mathematical formula based upon Darko farms limited’s (DF Ltd.) cost data:
y = mx +b
Darko Farms limited’s (DF Ltd.) overall cost is indicated as TC, a reliant variable, adopting
standard slope-intercept formulation, a linear formula. The algebraic formula is as follows:
TC = VC * Q + FC
Where,
Q = Annual production
TC = Total Price
VC = Cost Variable
3

Q = The number of properties created
FC = Fixed Price
b) Calculation of the profit or loss of Darko farms limited (DF Ltd.)
When estimating the earnings of Darko farms limited, two specific things must be taken into
account (DF Ltd.). The first represents the one-time fee of £120,000. Another is a variable cost,
which fluctuates according to two factors: the actual number of copies manufactured by the firm
as well as the expense of every entity. The yearly manufacturing is 800,000 units, with a variable
cost of £0.80 per unit. The corporation chose to charge £4.00 for each item.
Total Variable Cost = Variable Cost per unit * Total output
= 0.80 * 800,000
= 640,000
Total cost = Total Variable Cost + Total Fixed Cost
= 640,000+ 120,000
= 760,000
Total Revenue = Total output * Selling price per unit
=800,000 * 4.00
= 3,200,000
Profit = Total Revenue - Total cost
= 3,200,000 – 760,000
= 2,440,000
c) Five-year projection of Darko farms limited (DF Ltd.)
By their simplest primitive aspect, financial forecasting entails projecting revenue and
expenditures over the following seasons. As per Romero et al., (2018) “In typical cases, one such
prognosis might take into account both institutional and historical data, along with projections
regarding external economic factors.” Financial prediction refers to whatever method of
4

determining then estimating as to if a particular company will continue to operate in the
foreseeable term. While those three main financial pronouncements are typically anticipated
inside this full financial environment, one income pronouncement appears likely to represent the
most common financial projection. Two growing ratios may be required to forecast Darko Farms
Limited’s five-year estimate (DF Ltd.). Companies estimate a 5% rise in unit variable cost per
year, a 10% growth in total output per year, and a 3% increase in unit sales price per year.
Particular
s
2022 2023 2024 2025 2026 2027
TFC 120000 120000 120000 120000 120000 120000
TVC 640000 672000 705600 740880 777924 816820.2
TC 760000 792000 825600 860880 897924 936820.2
Q 800000 880000 968000 1064800 1171280 1288408
P 4 4.12 4.24 4.37 4.50 4.63
TR (Q*P) 3200000 3625600 4104320 4653176 5270760 5965329.04
Profit
(TR-TC)
2440000 2833600 3278720 3792296 4372836 5028508.84
Table 01: Darko farms limited (DF Ltd. Financial) ’s forecast for another five years
5

2022 2023 2024 2025 2026 2027
0
1000000
2000000
3000000
4000000
5000000
6000000
7000000
Darko farms limited (DF Ltd.
Financial)'s forecast for another five
years
TFC TVC TC Q
P TR (Q*P) Profit (TR-TC)
Chart 01: Darko farms limited (DF Ltd. Financial) ’s forecast for another five years
2022 2023 2024 2025 2026 2027
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Darko farms' pricing and profit
projections are restricted (DF Ltd.)
P Profit per unit
Chart 02: Darko farms’ pricing and profit projections are restricted (DF Ltd.)
6

d) Darko farms limited (DF Ltd.) costs and revenues assessment plus
commentary
Turnover refers to the revenues generated by a company during a specific time frame, for
instance, one year. This overall number of items supplied and the actual amount of those things
define the revenue generated. In a nutshell, earnings are equivalent to cost divided by quantity.
Profits are referred to as sales, sales profitability, selling market value, and increased revenues.
Costs are the costs spent during the overall manufacturing process of every product.
Corporations generate revenue via offering. Variable spending is those which vary based upon
the amount of revenue earned. Therefore, critical resource costs rise as the number of goods
supplied grows. Some costs, referred to as consistent spending, do not change irrespective of
extra revenue produced. Some spending, referred to simply ongoing costs, do not change
irrespective of the extra revenue produced. One example is a deed for whatever workspace, a
continuing expenditure that would never alter from item to item, notwithstanding increased
productivity. Preliminary and indirect charges were separated in certain mixed ways towards
classifying spending.
Operating costs, such as key components, can usually be traced directly to a single product,
although ancillary costs, such instance housing, can also be recognized. This percentage of
money necessary by every firm that generates a certain manufacturing amount is referred to as
total manufacturing expenditure. Total spending is made up of continuous and variable charges.
Revenue is characterized as the quantity of money left behind after all additional expenditures
have been covered. As per Nan and Tanriverdi, (2017) “Competitiveness is calculated by
deducting all expenses from income.” In its most basic form, profitability represents entire
revenues without entire expenses. Investment does hardly often provide a profit. Whenever sales
revenue becomes inadequate sufficient cover overall production costs, deficits occur.
As shown in table and chart one, the fixed cost is £120,000, constant throughout the economic
era. The yearly output in 2022 will be 800,000 units, up 10% from the previous year. The overall
output for 2027 stayed the same at 1,288,408. From 2022 to 2027, the unit variable cost
increased by 5% each year, rising from 640,000 to 816,820.2. The sale price was also raised by
3%, from $4.63 to $4.63 per unit. Darko farms limited (DF Ltd.) increased its earnings and
7

productivity. At the end of 2022, the profit was £2,440,000. By the end of 2027, the figure will
have risen to 5028508.84.
Question 02
1. Advertisement and revenues correlation analysis evaluation
Year Advertising
expenditure
(X)
(£000s)
Sales
revenue
(Y)
(£000s)
xy x2 y2
1 2016 2 60 120 4 3600
2 2017 5 90 450 25 8100
3 2018 4 70 280 16 4900
4 2019 6 100 600 36 10000
5 2020 3 80 240 9 6400
∑ xy =¿ ¿16
90
∑ x2=¿ ¿
90
∑ y2 =¿
33000
Table 02: Measuring the advertisement and earnings relationship
CorrelationCoefficient , r =n ¿ ¿
= ( 5∗1690 ) −(20∗400)
√ (5∗90−400)(5∗33000−160000)
= 450
500
= 0.9
8

Comments
An association value within -1 and +1 show whether two parameters are perfectly linearly
related. Such associated component would be a numerical expression that shows a significant
relationship among the oscillations among two variables. Each dynamic collection ranges from -
1 through 1. According to Vidgen et al., (2017) “Whenever the calculated number equals more
than 1 or less than -1, there is a major mistake in connection evaluation.” The flawlessly negative
relationship is symbolized by a correlation of -1, while a flawlessly positive linkage is expressed
with whatever value of 1. Whatever quantity of the correlation of 0 denotes implies no
proportionality linkages between the changes among these two variables. The producer of the
exercise equipment firm mentioned in the query has a correlation value of 0.9, which compounds
are in the range of -1 to +1. As just a consequence, two variables have a smooth linear
relationship: advertising spend and sales income are indicated by x, and sales revenue is
designated by y. To put it another way, if a manufacturer’s advertising budget grows, so does its
sales income, and conversely.
2. Advertisement expenditures and revenue income are depicted in a
scatterplot.
2015.5 2016 2016.5 2017 2017.5 2018 2018.5 2019 2019.5 2020 2020.5
0
20
40
60
80
100
120
Chart Title
Advertising expenditure (X) (£000s) Sales revenue (Y) (£000s)
Chart 03: Scattered chart with advertising spending is linked with store revenue.
9

The relationship between different elements is explored for both structures:
Scattered charts are a helpful technique for visually reviewing various varieties of material to see
if there is any link or association. This scatter diagram exhibits two sets of numerical statistics,
one per dimension, to investigate if there might be an association between them. These endpoints
can be located on any line or slope as long as these elements maintain contact. The closer these
endpoints follow that arc, the tighter the overall association. However, it is vital to know that
association often does not mean causation. As per Markovitch et al., (2020) “When statistics are
dispersed across a whole chart, it is difficult to guess how growth from one set of data led to an
expansion and collapse in the other - this might have been down to chance.” Either of these sets
of data might well be linked to everything else. Charts may also show a strong, negative, or zero
linkage. Another figure grows too whenever one variable climbs, suggesting a significant
association. Each has a good connection. An inverse relationship indicates that when one figure
rises, the other drops. Each has a poor relationship. If there is no association between those two
variables, there seem to be no relationships connecting them. In figure 03, a scatter diagram of
marketing expenditure and sales income is presented. The association between advertising
spending and sales income is depicted in the chart
3. Impact spending and sales are the subjects of a deep inspection and
suggestions
Marketing expenses’ impact on profitability
It is worth mentioning that a high rate of return on a promotional budget does not mean
automatically that a company is making a profit, as many other expenses must be subtracted
prior to estimating a corporation’s gross sales proportion. On the other side, that data
demonstrates the true underpinning relationship between marketing endeavors and sales.
According to Gunasekaran et al., (2018) “Return on investment ROAS may have been used to
compare the entire cost of any advertisement campaign to most others, factors that determine
how profitable an industry’s promotion is in terms of generating money.” For example, while
marketing effort “A” may ensure increased volume by two times as much as a marketing strategy
“B,” “B” is a more cost-effective marketing expenditure if strategy “B” costs half as much as
project “A.” Despite rising competitiveness, specialized promotion strategies may raise total
earnings. On the other hand, others may result in a substantial rise in gross profit even if sales are
10

only marginally higher. This might be because advertisement “B” assisted in the sale of products
with a broad range of income ratios.
Companies utilize product variety as a marketing plan to set their products apart from other
similar options. Whatever visual element, such as pace, strength, efficiency, or quality product,
could assist. This might also refer to a transient quality, such as superior and trendier than the
rivals. A portfolios segmentation strategy could give even small businesses a competitive
advantage in a market dominated by larger, more large entities.
There appear to be a number of complex factors that affect the whole consumer quandary
process. Male and females, for example, have quite varying needs and behaviors when it comes
to personal things as either a group. Solo and coupled people without children are more likely to
pick eateries that cater to families with younger children. A buyer having past purchasing
experience in a particular region may approach the decision differently as someone who has
never purchased anything.” Advertisements with a better understanding of such regulating
elements may make more accurate inferences about customer behavior.
The recommendation in the fitness sector for gaining a competitive edge
1. Make sure that the product or service meets the needs of the customer: Each company
executive must have had a solid understanding of their customers’ needs. Determining the
customer categories that will benefit the company and its products is part of the marketing
strategy. These are all the persons who appear to be most interested in becoming their
clientele. The methods to promote technique aids in restricting their desired demographic to
persons who are more prone to acquire (Power et al., 2018). As a result, it allows the
company to concentrate its finite sales efforts on reaching out to select important customer
categories instead of spending time attempting to reach out to people who do not regard their
product as an urgent need.
2. Take on the Developing Markets: Their marketing approach identifies possible sectors
where their company might join and get a foothold before competitors - an advantage known
as “first to market.” Emerging markets occur as a result of new factors such as shifting
demographics, customer demand patterns, or technological advancements that can be
transformed into newer commodities, and enterprises who succeed at marketing strategy get
11

the capacity to notice them. An effective marketing plan requires the ability to select the most
profitable opportunities from among many available.
3. The Advantages of Leveraging: The Advantages of Utilising Any effective advertising
strategy involves a well-crafted story that accurately and attractively expresses the firm’s
marketing tactical advantage over its competitors. Most convincing statements explain why
the firm’s services appear to be not simply more substantial than those provided by
competitors, but why they might be truly the greatest alternative. Customers should not be
required to compare pricing since they would not regard the offerings of competitors to be
comparable.
4. Expand the number of distribution points: Any small business may increase its odds of
closing a sale to a certain customer by providing additional possibilities for them to learn
about what they have to offer, which needs the inclusion of new distribution channels. A
southern barbecue establishment, for example, may have a food stall that goes around town.
By introducing a frozen BBQ meal line marketed in specialty shops, the business might
monetize its good name.
The need for consumer assistance should be addressed: Management must include customer help
in their strategy. Sustaining a happy customer leads to repeat business and the opportunity to
pass on word-of-mouth referrals to other potential customers. Customer assistance may be
transformed into a financial gain by swiftly resolving customer issues, having someone available
to continually connect with customers, valuing customers as individuals, and understanding how
effectively the company can improve its goods or services.
Question 03
a) Break-Even Point of Mansion Plc
Regarding institutional accounting, this break-even position technique is computed by
fragmenting total stable expenses associated with that manufactured income, apiece component
fewer variable spending regarding each component. As per Lee et al., (2020) “Continuing costs
must never change depending on the overall number of items provided throughout such a case.”
As we look at things from a different perspective, the break-even position appears to be the stage
at which a company’s total earnings equals its total expenditures.
12

I. Given,
Selling price per unit = 440,000
Variable cost per unit = 242,000
Fixed selling and Distribution Cost = 90,000+24,000
= 114000
Total Fixed cost = (Fixed Administration Cost + Fixed selling and Distribution
Cost)
= (50,000 + 114,000)
= 164,000
Break Even Point in Units = Fixed costs + (Sales Price per Unit – Variable Cost
per Unit)
= 164,000 + (440,000 - 242,000)
= 362,000
II. Given, Sales unit = 360,183
Margin of Safety (in Units) = Budgeted Units – Breakeven Unit
= 360,183 - 362,000
= -1,817
The overall turnover of just this company is less than 362,000, which constitutes the overall
break-even mark. Moreover, such risk buffer is reduced to zero. This means that this company
will not profit until it sells 362,000 units of its product, and it might be in the red for a long time.
There is no security buffer in place at Mansion Plc.
Margin of Safety Ratio = (Margin of safety in Units ÷ Sales in Units) * 100
= (-1,817 ÷ 360,183) * 100
= -0.50446578544
13

b) Evaluation discussion of Mansion Plc
The net financial approach provides a much more solid platform for determining the value of
one’s items. Examine a person’s present monetary condition and determine whether they are
prepared to endure until they achieve breather. This break-even assessment might very well
similarly be used to determine a company’s precise sales objectives. It is often easier to set
revenue targets whenever you have a certain amount as well as a period insight like Mansion Plc
did. It is worth looking at some unforeseen entrepreneurship notions. As per Koulopoulos and
Keldsen, (2016) “The Break-even model can help businesses reduce risk by steering them aside
towards activities or innovative products destined to fail.”
c) Factors Mansion PLC’s management should consider before committing
the company to the course of action
Every corporation defendant’s constitutional foundation should be thoroughly examined and
reported with depth just on the document. Due to this necessity to connect criminal violation to a
governing authority, evidentiary challenges might emerge when the organization under question
has a dispersed organization (Wang et al., 2019). The lesser the organization, the greater
probable it is because more managing executive, hence the organization, is responsible for
knowing anything bad. Mansion PLC’s management should promptly listen to their management
team conduct their business.
d) The study examines the benefits and downsides of employing the break-
even concept:
The gross-profit analysis gives a far stronger foundation for valuing one’s products. Evaluate an
individual’s current financial situation and decide whether one is willing to wait to reach the
break-even point. The break-even analysis may also be a useful tool for determining specific
revenue targets for a company (Griva et al., 2018). As Mansion Plc did, it is generally easier to
build income goals when one has a particular sum and a timeframe in mind. Some unintended
entrepreneurial concepts should be investigated. Break-even analysis can help companies
decrease risk by diverting them away from initiatives or product offerings likely to fail.
14

Conclusion
The first question shows that Darko farms limited earned their profit of £2,440,000 and their next
six-year projection from 2022 to 2027. In question, two advertisement expenditures and revenue
income are shown. Furthermore, finally in question, answers the financial dilemma Mansion
PLC faces.
15

References
1. Griva, A., Bardaki, C., Pramatari, K. and Papakiriakopoulos, D., 2018. Retail business
analytics: Customer visit segmentation using market basket data. Expert Systems with
Applications, 100, pp.1-16.
2. Gunasekaran, A., Yusuf, Y.Y., Adeleye, E.O. and Papadopoulos, T., 2018. Agile
manufacturing practices: the role of big data and business analytics with multiple case
studies. International Journal of Production Research, 56(1-2), pp.385-397.
3. Koulopoulos, T. and Keldsen, D., 2016. Gen Z effect: The six forces shaping the future of
business. Routledge.
4. Lee, M., Cai, Y.M., DeFranco, A. and Lee, J., 2020. Exploring influential factors affecting
guest satisfaction: big data and business analytics in consumer-generated reviews. Journal of
Hospitality and Tourism Technology.
5. Markovitch, D.G., Huang, D. and Ye, P., 2020. Marketing intensity and firm performance:
Contrasting the insights based on actual marketing expenditure and its SG&A proxy. Journal
of Business Research, 118, pp.223-239.
6. Mikalef, P., Pappas, I., Krogstie, J. and Pavlou, P.A. eds., 2020. Big data and business
analytics: A research agenda for realizing business value. Elsevier.
7. Nan, N. and Tanriverdi, H., 2017. Unifying the Role of IT in Hyperturbulence and
Competitive Advantage Via a Multilevel Perspective of IS Strategy. MIS Q., 41(3), pp.937-
958.
8. Power, D.J., Heavin, C., McDermott, J. and Daly, M., 2018. Defining business analytics: an
empirical approach. Journal of Business Analytics, 1(1), pp.40-53.
9. Romero, R., Franco, J.F., Leão, F.B., Rider, M.J. and De Souza, E.S., 2018. A new
mathematical model for the restoration problem in balanced radial distribution
systems. IEEE transactions on power systems, 31(2), pp.1259-1268.
10. Seddon, P.B., Constantinidis, D., Tamm, T. and Dod, H., 2017. How does business analytics
contribute to business value?. Information Systems Journal, 27(3), pp.237-269.
16

11. Vidgen, R., Shaw, S. and Grant, D.B., 2017. Management challenges in creating value from
business analytics. European Journal of Operational Research, 261(2), pp.626-639.
12. Wang, S., Yeoh, W., Richards, G., Wong, S.F. and Chang, Y., 2019. Harnessing business
analytics value through organizational absorptive capacity. Information &
Management, 56(7), p.103152.
17