Business Analytics and Operations Research

This document provides solutions to questions related to business analytics and operations research. It covers topics such as decision-making approaches, expected value, expected monetary value, maximum utility approach, seminar profitability, and hypothesis testing. The document includes calculations, tables, and references.

JNB535 / BUSINESS
ANALYTICS AND
OPERATIONS RESEARCH

Table of Contents
Question: 1.......................................................................................................................................3
Question: 2.......................................................................................................................................4
Question: 3.......................................................................................................................................5

Question: 1
a.
Service
Demand for services
Strong (maximum
profit)
Average (average
profit)
Weak (Minimum
profit)
Full price 950 350 50
Discount price 680 470 310
If optimistic approach would be adopted then full price service would be recommended due to
higher profitability of 950 than 680, where as in case of conservative approach, the
recommended service would be discount service as again the profitability is higher with
discount service in the event of average and weak demand.
To determine the decision through minimax approach, the following regret table has been
prepared:
Service Strong demand Average demand Weak demand Maximum
regret
Full price 0 120 260 260
Discount price 270 0 0 270
Therefore, by applying the minimax approach, the recommended decision would be full price
service.
b. Through the application of expected value approach the optimal decision can be derived as
follows:
Expected value of full price services = 0.3*950 + 0.45*350 + 0.25*50 = 285 + 157.5 + 12.5 =
455
Expected value of discount price services
= 0.3*680 + 0.45*470 + 0.25*310 = 204 + 211.5 + 77.5 = 493
Therefore, an optimal decision is discount price services as the expected value of profit is higher
in case of discount price services.
c.

By applying the concept of expected monetary value, the above decision tree has been created.
The outcome with the highest expected monetary value will be chosen. The tree starts with two
choices that is, full price or discount price services and the forecasted profits are multiplies by
the probability of their occurrence that is for strong demand it is 0.3, average demand 0.45 and
weak demand 0.25. The each service’s expected value is summed up to obtain the expected
monetary value of each service (Fox and Bauldry, 2020). Discount price services has highest
expected monetary value, therefore this choice will yield more profits.
d. Maximum utility approach
Point estimate for probability of strong demand = 0.30+0.38/2 = 0.34
Point estimate for probability of average demand = 0.40+0.46/2 = 0.43
Point estimate for probability of weak demand = 0.20+0.27/2 = 0.235
Services Strong Average Weak Utils
Full price 0.34 * ln(950) =
2.33
0.43 * ln(350) =
2.52
0.235 * ln(50) =
0.92
=
(2.33+2.52+0.92)
* 0.56
= 5.77 * 0.56
= 3.23
=25.28 utils
discount 0.34 * ln(680) =
0.34 * 6.52
= 2.22
0.43 * ln(470) =
0.43 * 6.15
= 2.64
0.235 * ln(310)
= 0.235 * 5.74
= 1.35
=
(2.22+2.64+1.35)
* -0.425
= 6.21 * (-0.425)
= -2.64
= 0.0714 utils
The maximum expected utility derived from full price service is positive and higher than lower
than one utils derived from discount price service.
e.

Question: 2
a)
Particulars Amoun
t
Number of individual per seminar (a) 30
Probability of an attendee opening an account (b) 0.03
Commission for each new account (c) 5500
Total commission per seminar d = a*b*c 4950
Cost per seminar 3800
Profit per seminar 1150
Expected value approach has been used for calculating expected profit for Genius investment
services (Conboy and et.al., 2020). This method involves calculation of expected profit by
multiplying total commission received by the company with the probability of converting the
lead so generated into a potential customers.
d)
Particulars Amoun
t
Number of individual per seminar (a) 30
Probability of an attendee opening an account (b) 0.0231
Commission for each new account (c) 5500
Total commission per seminar d = a*b*c 3811.5
Cost per seminar 3800
Profit per seminar 11.5
If there is a probability of an attendee opening an account will be equals to 0.0231 (calculated
using trial and error method with excel) which indicates that even one attendee out of 30
attendees if open their account will results in company’s average profit greater than zero.
Question: 3
a) Null hypothesis = Mean = population mean; x̄ = μ
Alternative hypothesis = Mean ≠ population mean; x̄ ≠ μ
The null hypothesis states above indicates that both the population mean that is 101.5 derived
from the number of email sent and received by the corporate employees is equal to the sample
mean of number of email sent and received by 10150 randomly selected federal employees.
While the alternative hypothesis states above indicates that there is a difference between the
mean number of email sent and received by corporate employees from that of federal employees
that is, sample mean and population mean is not equal.
b) Testing the hypothesis at a significance level of 0.01.

Population mean = 101.5 given
Sample mean = 100.46 calculated using excel
Standard deviation of population = 24.96
Standard deviation of sample = 24.97
Alpha = 0.01 significance with 99% confidence level
N = 10150
Z = x̄ - μ / σ √n
Z= 100.46 – 101.5 / 24.96 √10150 = -1.04 / 2514.72 = - 0.0004
Z score at 0.01 significance level = 2.58
So, as the calculated value of zcal < 2.58 then the null hypothesis has been accepted as per the rule
of hypothesis acceptance which states that if the calculated value of z is greater than the value of
z score, then null hypothesis will be rejected and if the calculated value of z is less than the value
of z score than the null hypothesis can’t be rejected (Kraus, Feuerriegel and Oztekin, 2020).
c) The non-rejection or acceptance of null hypothesis reflects that there is no difference between
the mean number of email sent and received by federal employees and corporate employees.

REFERENCES
Kraus, M., Feuerriegel, S. and Oztekin, A., 2020. Deep learning in business analytics and
operations research: Models, applications and managerial implications. European
Journal of Operational Research, 281(3), pp.628-641.
Conboy, K., and et.al., 2020. Using business analytics to enhance dynamic capabilities in
operations research: A case analysis and research agenda. European Journal of
Operational Research, 281(3), pp.656-672.
Fox, W. P. and Bauldry, W. C., 2020. Advanced Problem Solving Using Maple™: Applied
Mathematics, Operations Research, Business Analytics, and Decision Analysis. Chapman
and Hall/CRC.