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EBUS305 Business Analytics and Big Data Management

Mock Exam Paper

The exam paper includes three questions, only two of which must be selected and answered. All questions carry equal weighting. Please make sure to show your workings and calculations in detail, where relevant.

Question 1. An insurance company is offering two new packages to its customers: life insurance and mortgages. Every application for any of the two packages must 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 number 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 £30 per unit on life insurance and £40 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 mathematical model.

b) Solve the model to determine the quotas to maximize the total expected profit.

c) List and describe the key assumptions of a linear programme.

Question 2. In August, a bookstore must decide how many of next year’s calendars should be ordered. Each calendar costs the store £2 and is sold for £3. After 1st January, any unsold calendars are returned to the publisher for a refund of £1 per calendar. The bookstore assumes that the number of calendars sold by 1st January follows the probability distribution shown in the table below. The store intends to order 200 calendars in August and wishes to calculate the expected net profit by performing a simulation.

Number of calendars sold	Probability
100	30%
150	20%
200	30%
250	15%
300	5%

a) Perform four replications of a simulation model using the random number stream 18, 56, 85 and 70 to generate demand, and compute a 90% confidence interval around the expected net profit. Use a test statistic value equal to 2.4. Show all the steps and calculations.

(40 marks)

b) The bookstore is unsure whether to go with an order size of 200 calendars and have conducted a simulation experiment with an order size of 250, performing 10 replications for each using the same random number stream. The results of the simulations are shown in the table below, where the cells under each replication show the expected net profit.

Replication	1	2	3	4	5	6	7	8	9	10
Order size = 200	0	200	0	200	0	100	100	0	200	200
Order size = 250	-50	150	-50	150	-50	50	50	-50	250	150

Compare the two alternatives using a 95% (with a test statistic value equal to 2.3) and 98% (with a test statistic value equal to 2.8) and suggest which option the company should opt for in either case.

(30 marks)

c) Describe the steps of a simulation study, and state what the limitations of simulation models may be.

Question 3. A walk-in clinic that has opened at 9am has received six patients within the first hour. After initial checks, the following decisions were made on each of the six patients:

Patient ID	Age (years)	Rate (bpm)	Cough?	Fever?	Sore Throat?	Decision
001	37	95	Yes	No fever	Yes	Admit
002	18	82	No	High fever	No	Admit
003	44	65	Yes	Low fever	No	Send home
004	72	85	No	No fever	Yes	Send home
005	25	92	Yes	High fever	Yes	Admit
006	52	84	Yes	No fever	No	Send home

A new patient has just walked in and was checked in with the details below. The clinic would now like to make a decision on the basis of the above data.

Patient ID

Age (years)

Rate

(bpm)

Cough?

Fever?

Sore

Throat?

Decision

007

High fever

Yes

a) Using only the variables Age and Heart Rate, develop and visually show a linear classifier, using which make a decision on Patient ID 007. Do you recommend this approach?

b) Using all variables Cough, Fever and Sore Throat, classify Patient ID 007 using the k- Nearest Neighbour Algorithm with values k = 1 and 3.

c) Describe the ways in which clustering differs from classification and give a practical example where a clustering approach would be needed. In your example, clearly state why clustering would be the right approach and which clustering technique would be most appropriate for this purpose.