CPA › Quantitative Analysis › May 2018

CPA Quantitative Analysis – May 2018 Past Paper & Answers

Unit: Quantitative Analysis

15 Questions

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Questions

Download CPA Quantitative Analysis May 2018 past paper with detailed answers and marking scheme. This paper is based on KASNEB examination standards and is ideal for revision and exam preparation.

Access the full paper online, download the PDF, or study offline. Each question includes step-by-step solutions to help you understand key concepts in Quantitative Analysis.

1a

Linear programming

Enumerate four assumptions that are implied in the application of the linear programming model.

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1b

Mathematical Techniques - Calculus

The unit price and total cost functions associated with the production and sale of a certain electric component are given by the following equations:

P = 100 - 5q

and

TC = q² + 4q + 300 (in thousands of shillings)

Where: P is the unit price of the electric component.

q is the number of electric components produced and sold.

TC is the total cost.

Required:

(i) The number of electric components that would maximise profit.

(ii) The maximum profit.

(iii) The maximum total revenue.

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1c

Mathematical Techniques - Matrix Algebra

A certain firm has three main departments namely; steel, motor vehicles and construction. The three departments are interdependent. Each unit of output from the steel department requires 0.2, 0.3 and 0.4 units from steel, motor vehicles and construction departments respectively. Each unit of output from motor vehicles department requires 0.2, 0.4 and 0.2 units from steel, motor vehicles and construction departments respectively. A unit of output from the construction department requires 0.3, 0.4 and 0.1 units from steel, motor vehicles and construction departments respectively. The final demand of the firm comprises 20 million, 50 million and 30 million units of output from steel, motor vehicles and construction departments respectively.

Required:

(i) The technical coefficient matrix.

(ii) The total output of each department given that the Leontief's inverse matrix is as provided below:

\(\frac{1}{0.192}\) \(\begin{bmatrix} 0.46 & 0.24 & 0.26 \\ 0.43 & 0.60 & 0.41 \\ 0.30 & 0.24 & 0.42 \\ \end{bmatrix}\)

(iii) The change in the total output of the construction department, given that the final demand of steel department decreases by 2 million units and that of motor vehicles department increases by 10 million units whereas that of the construction department does not change.

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2a

Decision Theory

(i) Distinguish between a "single server queuing model" and a "multiple server queuing model".

(ii) Highlight two assumptions of the queuing theory.

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2b

Decision Theory

Outline three advantages and three disadvantages of the simulation model as used in quantitative analysis.

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2c

Hypothesis Testing and Estimation

Mwanaisha Ali sells tree seedlings at Mavuno market. A random sample of 9 of the seedlings had the following height in centimetres:

64 62 65 63 68 69 65 63 65.

Required:

A 95 per cent confidence interval of the population mean height of the seedlings.

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2d

Mathematical Techniques - Calculus

BC Limited operates two factories namely; X₁ and X2. Both factories deal in the production of a product named "Nguzo". The joint cost function for production of product "Nguzo" is given by:

\(C = f(q_1, q_2) = 2q_1^2 + q_1q_2 + q_2^2 + 500\)

Where: C = Joint cost function of factories X₁ and X₂

\(q_1\)

= Quantity produced by factory X₁

\(q_2\)

= Quantity produced by factory X₂

BC Limite has received an order to produce 200 units of product "Nguzo".

Required:

The quantities of product "Nguzo" that should be produced by factories X₁ and X2 respectively in order to minimise cost.

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3a

Hypothesis Testing and Estimation

Explain the difference between the following sets of terms as used in hypothesis testing and estimation:

(i) "Type 1 error" and "type II error".

(ii) "One tailed test" and "two tailed test".

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3b

Hypothesis Testing and Estimation

Faida Limited deals in the manufacture and sale of a product named "Big". The company sells the product in two of its distribution outlets, A and B.

The data below relate to a random survey of monthly mean sales of the product in the two outlets:

Outlet	Monthly mean sales (Sh."000")	Standard deviation (Sh."000")	Sample size
A	795	50	200
B	810	70	175

Required:

Test at a 5 per cent level of significance, whether there is a significant difference in the monthly mean sales of the two outlets.

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3c

Decision Theory

A manufacturing company is considering production of one of the three different types of pens, P₁, P₂ and P3. The fixed and variable costs of producing the pens are as given below:

Type of pen	Fixed cost (Sh.)	Variable cost (Sh.)
P1	2,000,000	100
P2	3,200,000	80
P3	6,000,000	60

The demand of the pens unde. three different states of demand is provided below:

State of demand	Number of pens
Low	250,000
Moderate	1000,000
High	1,500,000

The unit se lling price of the pens is Sh.200.

Required:

(i) The payoff table of the company.

(ii) The type of pen to produce using the maximin criterion.

(iii) The type of pen to produce using the maximax criterion.

(iv) The type of pen to produce using the minimax regret criterion.

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4a

Decision Theory

Define the following terms as used in game theory:

(i) Mixed strategy.

(ii) Value of the game.

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4b

Correlation Analysis

An intelligence test was undertaken by ten sales ladies of a certain company.

The table below shows the intelligence test scores in percentages and the mean weekly sales in thousands of shillings made by the salesladies:

Saleslady	1	2	3	4	5	6	7	8	9	10
Intelligence test score (%)	40	70	50	60	80	50	90	40	60	60
Weekly sales (Sh. "000")	50	120	80	100	80	50	110	60	90	60

Required:

The coefficient of correlation. Interpret your result.

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4c

Linear programming

A firm manufactures two products, X and Y, subject to constraints on three raw materials, RM1, RM2 and RM3. The objective of the firm is to select a product mix that will maximise weekly profit. Each unit of product X earns a profit of Sh.2 whereas each unit of product Y earns a profit of Sh.1.

Details of the raw materials required for the production of products X and Y are as given below:

Raw material	Maximum quantity	Quantity required per unit of production
	(units)	Product X	Product Y
RM1	27	3	0
RM2	30	0	2
RM3	20	1	1

Required:

(i) A linear programming model of the firm.

(ii) The optimum product mix using the simplex method.

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5a

Probability

An electricity company has established that the weekly number of occurrences of lightning striking transformers follows a Poisson distribution with a mean of 0.4 per week.

Required:

(i) The probability that no transformer will be struck by lightning in a week.

(ii) The probability that at most two transformers will be struck by lightning in a week.

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5b

Decision Theory

The following information relates to a certain construction project:

Activity	Preceding activity	Time estimates (weeks)
		Most optimistic	Most likely	Most pessimistic
A	-	2	4	12
B	-	10	12	26
C	A	8	9	10
D	A	10	15	20
E	A	7	7.5	11
F	B,C	9	9	9
G	D	3	3.5	7
H	E,F,G	5	5	5

Required:

(i) The network diagram for the project.

(ii) The critical path.

(iii) The probability of completing the project within a 30 - week duration.

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