KASNEB Quantitative Analysis - Question 2a

Distinguish between a 'univariate function' and a 'multivariate function'.... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 3a

Explain the following terms as used in game theory:(i) Pay-off.(ii) Value of a game.... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 3b

Highlight eight steps followed in the simulation process.... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 5a

Outline three differences between the normal distribution and the t-distribution.... [Click to view full question and step-by-step solution]

May 2016

Q: KASNEB Quantitative Analysis - Question 1c

Shujaa Limited deals in the manufacture of a product named 'Zed'. The product 'Zed' is produced on order and the company does not keep inventory of the produ... [Click to view full question and step-by-step solution]

1a

Decision Theory

Explain four differences between the project evaluation and review technique (PERT) and the critical path analysis (CPA).

1b

Mathematical Techniques - Matrix Algebra

A certain audit firm has two categories of employees, auditors and assistant auditors. The total monthly salary of I auditor and 5 assistant auditors amount to Sh.456.755 whereas the total monthly salary of 3 auditors and 9 assistant auditors amount to Sh.985,005. The firm has a total of 6 auditors and 14 assistant auditors. The employees contribute 12 per cent of their monthly salaries towards their sacco society.

Required:
(i) The monthly salary of an auditor and an assistant auditor, using matrix algebra,
(ii) The employees' total monthly contribution towards their sacco society.

1c

Mathematical Techniques - Calculus

Shujaa Limited deals in the manufacture of a product named "Zed". The product "Zed" is produced on order and the company does not keep inventory of the product. The demand and total cost functions (in thousands of shillings) of the company are given as follows:

P = 190 - q

and

TC = q² + 10q + 500

Where:

P is the unit selling price.

q is the quantity demanded in units.

TC is the total cost.

Required:
(1) The maximum profit of the company.
(ii) The output level that would maximise total revenue.

2a

Mathematical Techniques - Functions

Distinguish between a "univariate function" and a "multivariate function".

2b

Probability

The mean weight of 500 packaging tins from a production process are normally distributed with a mean weight of 151 grammes and a standard deviation of 15 grammes.

Required:
(i) The number of packaging tins that weigh between 120 grammes and 155 grammes.
(ii) The number of packaging tins that weigh more than 185 grammes.

2c

Time series

The following data were obtained from the records of Kiwandani Limited for the year 2015:

Month
January
February
March
April
May
June

Total
overhead cost (y)
(Sh.)
16,250
15,000
15,000
14,500
15,250
15,750

Director labour
hours (x)

1,056

736
840
800
880

1,008

Required:
(i) The least squares regression function relating direct labour hours and total overhead cost.
(ii) The coefficient of determination. Comment on your result.

3a

Decision Theory

Explain the following terms as used in game theory:

(i) Pay-off.
(ii) Value of a game.

3b

Decision Theory

Highlight eight steps followed in the simulation process.

3c

Correlation Analysis

The table below shows the actual sales and target sales of eight sales agents for the year 2015 in millions of shillings.

Sales agent

Actual sales (y)
Target sales (x)

1

45
40

2

41
27

3

50
45

4

56
38

5

60
52

6

42
35

7

43
29

8

52
44

Required:
The Spearman's rank correlation coefficient. Interpret your result.

3d

Decision Theory

A cashier at a departmental store can serve on average 24 customers per hour. The arrival rate of customers averages 20 customers per hour. The departmental store applies a single channel queuing system.

Required:
(i) The probability that the cashier is idle.
(ii) The average number of customers in the queuing system.
(iii) The average time a customer spends in the queue waiting to be served.

4a

Decision Theory

Viwanda Limited deals in the production of a product named "Nguvu". The production cost of the product is Sh.500 per unit (excluding packaging cost). The product is sold at Sh.1,000 per unit. The company is considering the purchase of one out of three different packaging systems. The cost data for the three packaging systems are as follows:

Packaging system

A
B
C

Purchase cost
Sh. "000"
100
200
400

Variable cost per
unit of product
Sh. "000"
1.50
1.00
0.50

Scrap value
Sh. "000"
10
20
40

All the three packaging systems have a useful life of one year after which they would be sold at their estimated scrap values. The probability distribution for the demand for product "Nguvu" is as provided below:

Demand (units)
100
200
400

Probability
0.3
0.6
0.1

Required:
Recommend the packaging system that should be purchased by Viwanda Limited

4b

Linear programming

Farm Produce Limited is a producer and distributor of maize flour. The company owns milling plants in Eldoret, Nanyuki and Narok towns. The milling plants have not been able to meet the demand orders of the company’s distribution offices located in Mombasa, Kisumu, Nairobi and Isiolo towns. The company is considering the construction of a new milling plant either in Nakuru town or Meru town, in order to expand its production capacity. The data below relate to the company’s production and demand requirements.

Milling plant

Eldoret
Nanyuki
Narok

Monthly
output (units)
30,000
12,000
28,000

Unit production
cost (Sh.)
96
100
104

Distribution office
Mombasa
Kisumu
Nairobi
Isiolo

Monthly demand (units)
20,000
24,000
30,000
18,000

Additional information:

The estimated unit production costs in Nakuru and Meru towns are Sh.98 and Sh.106 respectively.

The unit transportation costs (in shillings) from each milling plant to each distribution office are given as follows

To
From	Eldoret Nanyuki Narok	Mombasa 64 56 58	Kisumu 36 52 42	Nairobi 52 44 36	Isiolo 58 32 50

The estimated unit transportation costs (in shillings) from each of the proposed milling plants to each distribution office are as follows:

To
From	Nakuru Meru	Mombasa 60 62	Kisumu 46 56	Nairobi 40 46	Isiolo 52 28

Assume that the construction of one of the proposed milling plants would satisfy the demand deficiency

Required:

Using the Vogel's approximation method (VAM), advise the management of Farm Produce Limited on the best location to construct the milling plant.

5a

Hypothesis Testing and Estimation

Outline three differences between the normal distribution and the t-distribution.

5b

Decision Theory

A certain project is expected to be completed within 18 weeks. The expected net revenue if the project is complete on time is Sh.1,120,000 but a penalty of Sh.484,000 will be imposed if the project is not completed on time. The cost of the project is Sh.459,000. The standard deviation of the project's duration is 2.08 weeks.

The table below is a summary of activities required to complete the project, the duration of the activities and their preceding activities.

Activity

A
B
C
D
E
F
G
H

Duration
(weeks)
5
2
4
2
5
7
6
3

Preceding activity

-
-
-
B
B, C
C
A, D
G, D, E, F

Required:
(i) A network diagram of the project.
(ii) The float times of activities B and D.
(iii) The critical path of the project.
(iv) A 95 per cent confidence interval of the expected completion time of the project.
(v) The expected profit from the project.

May 2016

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