CPA › Quantitative Analysis › November 2016

CPA Quantitative Analysis – November 2016 Past Paper & Answers

Unit: Quantitative Analysis

14 Questions

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Questions

Download CPA Quantitative Analysis November 2016 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.

Other Quantitative Analysis Past Papers

1a
Linear programming
​​Explanation of the following terms as used in Linear programming

(i) Infeasibility.
(ii) Unboundedness.
(iii) Alternate optimality.
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1b
Probability
​​The following information relates to product "X" which is susceptible to three types of defects; A, B and C. The probability of product "X" containing defect C depends on whether the product contains any other defects, A or B. The probabilities of the product containing the defects are as follows:
Type of defect
Probability
A
0.15
B
0.14
C(if it neither contains defect A nor defect B)
0.3
C(if it contains either defect A or defect B)
0.2
C(if it contains both defects A and B)
0.1

Required:
(i)      The probability that product "X" contains no defect.
(ii)     The probability that product "X" contains only one of the three defects
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1c
Hypothesis Testing and Estimation
​​The data below show the number of students enrolled in six colleges for a certain course, before and after the course was advertised in a certain publication:
College
Number of students
 before advertisement
Number of students
after advertisement
1
165
170
2
140
141
3
143
142
4
160
167
5
162
168
6
154
157

Required:
Using the paired t-test, determine whether the advertisement was a success at a 5 per cent level of significance.
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2a
Decision Theory
​​Highlight four applications of Markov analysis in business.
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2b
Probability
​ ​ ​​Faidika College offers three courses, namely; Accounting, Information Technology and Statistics. The marketing department of the college conducted a survey on 500 students to determine the number of students enrolled for each of the three courses. The results of the survey were as follows:

  • 329 students were enrolled for Accounting.
  • 186 students were enrolled for Information Technology.
  • 295 students were enrolled for Statistics.
  • 83 students were enrolled for Accounting and Information Technology.
  • 217 students were enrolled for Accounting and Statistics.
  • 63 students were enrolled for Statistics and Information Technology.

Required:
(i) Illustrate the above information in a venn diagram.
(ii) The probability that a student is enrolled for all the three courses.
(iii) The probability that a student is enrolled for Accounting or Statistics but is not enrolled for Information Technology
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2c
Regression Analysis
​ ​​

The following data show results of a regression run on the variations in labour cost as a function of labour hours worked in a certain company:

Regression statistics

R-squared
X1
Multiple R
X2
Standard error
0.7320
Observations
24

ANOVA

Degrees of freedom (DF) Sum of squares (SS) Mean square (MS) F-ratio Significance F
Regression
 X3
 0.029
       0.029
 X5
 0
Residual or error
 22
         X4     
 0.000455
Total
 23
  0.04

Coefficients

Coefficients Standard error t-statistic P-value
Intercept
 0.077
 X6
 11.328
 0
Slope
 0.826
 0.103
 X7
 0

Required:

  1. The missing values of X1, X2, X3, X4, X5, X6, and X7.
  2. A 95 per cent confidence level of the labour hours worked.
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3a
Linear programming
​ ​​TOC Limited, an oil prospecting company, intends to set up two oil refineries, refinery I and refinery II.

The following information relates to TOC Limited:
1. The company will produce two types of fuel; diesel and petrol, in each of the two refineries.
2. Three types of resources namely; crude oil, furnace time and mixer will be required to produce each litre of fuel.
3. The resource requirements for each of the two refineries is as follows:  

Fuel per litre
Crude oil
(litres)
Furnace time
(hours)
Mixer
(litres)
Diesel (Refinery I)
3
2
8
Petrol (Refinery I)
1
1
6
Diesel (Refinery II)
3
1
7
Petrol (Refinery II)
2
1
5

4. The daily amount of crude oil available at the two refineries are 12,000 litres and 15,000 litres for refinery I and refinery II respectively.
5. The hours of furnace time available at the two refineries are 10 hours and 4 hours for refinery I and refinery II respectively.
6. The total amount of mixer available for use at the two refineries is 80,000 litres per day.
7. The fuel is expected to be sold at Sh.170 per litre of diesel and Sh. 160 per litre of petrol.
8. All fuel produced is expected to be sold to a sole distributor. It will cost Sh.80 to transport each litre of fuel from refinery I and Sh. 100 from refinery II to the sole distributor.
9. Assume that crude oil cannot be transported from one refinery to another.

Required:
Formulate a linear programming model to maximise TOC Limited's revenue, assuming that only transport cost is variable.

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3b
Time series
​ ​ ​ ​ ​ ​​The following data show quarterly production of oranges by a certain large scale farmer in thousands of kilogrammes:

Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4
2012
250
200
180
300
2013
330
280
260
380
2014
410
370
340
460
2015
478
-
-
-

Required:
(i).  The adjusted seasonal component for the four quarters using the additive model.
(ii). The deseasonalised production data for each quarter.
(iii). Explain the significance of the deseasonalised data.
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4a
Linear programming
​​Enumerate four limitations of linear programming models.
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4b
Decision Theory
​​Summarise four decision criteria used in decision making under uncertainty.
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4c
Mathematical Techniques - Calculus
​​An electronics company sells programmable calculators at a unit price of Sh.100. Studies indicate that the company can sell additional 100 calculators per year for Sh.5 decrease in unit price and 100 calculators per year less for Sh.5 increase in unit price. The company currently sells 3,000 calculators per year. The cost function of the company is assumed to be linear with a fixed cost of Sh.10,000 and variable cost of Sh.65 per calculator.

 Required: 
(i) The price and quantity that would maximise profit. 
(ii) The maximum profit.
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4d
Decision Theory
​ ​​A barber shop has a total of 10 available seats for customers. The inter-arrival times for customers are exponentially distributed with an average of 20 customers arriving each hour. Any prospective customer who finds all the seats occupied does not wait for service but instead leaves. The barber takes an average of 12 minutes to cut each customer's hair. Hair cut time duration is exponentially distributed.

Required:
(i) The average number of hair cuts that will be completed by the barber each hour. 
(ii) The average time each customer will spend at the barber shop.
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5a
Decision Theory
​​Outline five limitations of game theory.
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5b
Decision Theory
​​The data below relate to activities of a certain project that is to be undertaken by Ujuzi Consultancy Company:

     Time (weeks)
Activity
Preceding
activity
Optimistic
Most probable
Pessimistic
A
-
1.5
2.0
2.5
B
A
2.0
2.5
6.0
C
-
1.0
2.0
3.0
D
C
1.5
2.0
2.5
E
B,D
0.5
1.0
1.5
F
E
1.0
2.0
3.0
G
B,D
3.0
3.5
7.0
H
G
3.0
4.0
5.0
I
F,H
1.5
2.0
2.5

Required:
(i).   A network diagram of the project.
(ii).  The expected completion time of the project.
(iii). The probability that the project will be completed between 13 weeks and 17 weeks
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