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UNIVERSITY OF SOUTHAMPTON MANG1019 W1
SEMESTER 1 EXAMINATIONS 2022-23
FOUNDATIONS OF BUSINESS ANALYTICS
DURATION: 180 MINUTES (3 HOURS)
This paper contains 5 questions.
Answer 4 questions in total. Each question is worth 25% of the final
exam mark and each question is marked separately up to 100%. An
outline marking scheme is shown in brackets to the right of each
question.
All questions carry equal marks.
If you attempt more questions than required, only the required
number of answers will be marked. Please strike through any
answers that you do not wish to be marked. If you do not do this the
marker will mark the answers in the order that they appear in your
exam booklet(s).
You must answer FOUR questions.
Please use a separate answer booklet for each section.
Only University approved calculators may be used.
A foreign language direct ‘Word to Word’ translation dictionary (paper
version) ONLY is permitted provided it contains no notes, additions
or annotations.
Normal Distribution Tables will be provided.
MANG1019 W1
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Q1. The R&D department of Protonics Ltd. has come up with a new
product which would make a useful addition to the company’s
existing product range. Demand for the product is uncertain but could
be characterised as either ‘high’ or ‘low’. If demand for the new
product is high, the company could either invest in additional
production capacity or work overtime. A low level of demand can be
met with existing production capacity and no overtime.
The management of Protonics has decided to start selling the new
product but is considering two main options for production:
(1) To invest immediately in additional production capacity, or
(2) To maintain existing production capacity and overtime if
necessary to meet demand; and then to invest in additional
production capacity after one year if demand for the new product
is ‘high’ during the first year.
Immediate investment costs are estimated at ￡500,000, while
investment after one year would cost ￡600,000.
In each year over the next five years, the annual net cash flow (in ￡
000s) with respect to Options 1 and 2 are estimated to be as shown
in the table below.
Production capacity ‘Low’ demand ‘High’ demand
With additional capacity 100 400
Existing capacity plus
overtime if necessary
150 200
Protonics’ management is not sure of the chance of high demand for
the new line in the first year. But if demand is high in the first year,
management considers that there will be a 70% chance of high
demand continuing throughout years 2-5. Similarly, if demand is low
in the first year, management considers that there will be a 70%
chance of low demand continuing throughout years 2-5.
All monetary values are expressed in present value terms.
MANG1019 W1
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(a) Draw a decision tree showing the options available to Protonics.
Show clearly the options after one year.
[70 MARKS]
(b) Let the probability of a high demand for the new line in the first
year be p. What the value of p is better to delay the decision
than invest immediately
[30 MARKS]
Q2. On a production line, the statistical control process involves
taking a random sample of 30 items and inspecting them for defects.
If more than five of the sampled items are found to have defects, the
production process stops and ALL items are inspected. There is an
11.5% chance that a randomly selected item has a defect; and it is
assumed that individual items may have defects independently of
other items.
The total cost to the company if the production line is stopped
completely so that ALL items can be inspected is ￡5, 000.
(a) Which probability distribution is most appropriate for modelling
this process Explain your answer.
[40 MARKS]
(b) Based on your answer in (a), calculate the expected cost to the
company of stopping the production line so that all items can be
inspected.
[60 MARKS]
TURN OVER
MANG1019 W1
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Q3. An insurance company is offering two new packages to its
customers: life insurance and mortgages. Every application for any
of the two packages has to go through three departments for
approval, namely underwriting, policy issue and administration, and
claims. The amount of work (in hours) required for each package (per
unit) in each department is given in the table below.
Department Life Insurance Mortgage
Underwriting 6 4
Policy issue and administration 2 3
Claims 2 0
Based on the number of staff in each department, the amount of
work-hours available for the underwriting, policy issue and
administration, and claims departments are calculated to be 1200,
600 and 300 hours, respectively. The expected profit is estimated to
be ￡3 per unit on life insurance and ￡4 per unit on mortgages. The
management wishes to establish sales quotas for the new packages
to maximize their total expected profit.
(a) Formulate the problem as a linear programme
[50 MARKS]
(b) Use the graphical method to solve the LP.
[50 MARKS]
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Q4. The manager of a restaurant thinks that the average distance in
miles travelled by their customers is over 20 miles. Therefore, the
manager of a restaurant has carried out a small-scale survey to find
out how far customers travel to the restaurant. The results for a
randomly selected sample of 8 customers were as follows (distances
in miles):
12, 23, 14, 27, 14, 8, 19, 27
(a) Compute the sample mean and the sample variance.
[10 MARKS]
(b) Formulate the null hypothesis and the alternative hypothesis
to test the manager’s hypothesis.
[30 MARKS]
(c) With a 5% significance level and using these sample
variance as the population variance, i.e, using the normal
distribution tables rather than the t-test, explain whether or
not the null hypothesis is rejected and what conclusion you
would get.
[60 MARKS]
Q5.
a) The results below are from a regression analysis carried out
using Excel.
Coefficients Standard Error t Stat P-value
Intercept -432 185 -2.33513514 0.101671
X Variable 1 42.25 7.603453163 5.55668577 0.011497
Write down the regression equation for these data.
[25 MARKS]
TURN OVER
MANG1019 W1
b) In regression, what is means by the total sum of the squares of
errors and the explained sum of the square of errors. How do these
relate to the coefficient of correlation
[25 MARKS]
c) Explain the difference between the mean squared error (MSE)
and the mean absolute deviation (MAD) when trying to decide how
to measure the line of best fit to a set of data.
[25 MARKS]
d) What are the assumptions of linear regression
[25 MARKS]
END OF PAPER
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