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Bme 500: Quantitative Methods For Managers Question Paper

Bme 500: Quantitative Methods For Managers

Course:Master Of Business Administration

Institution: Kenyatta University question papers

Exam Year:2011

DATE: TUESDAY, 29TH MARCH 2011 TIME: 5.30 P.M. - 8.30 P.M.

Instructions
Time Allowed: 3 hrs
Answer question one and any other three questions
Use of practical examples to elaborate your points is highly encouraged

Question 1
Sarajevo farmers society are involved in selling of four types of produce: Maize, Potatoes, Carrots
and tomatoes in each of the two towns- Nakuru and Mombasa to three classes of customers. These
are consumers, wholesalers and retailers who buy in bags as given below:
Nakuru:

Maize Potatoes Carotts
Tomatoes
Consumers 4
6
7
4
Retailers
3
2
1
6
Wholesalers 4
3 5 3

Mombasa:
Maize Potatoes Carotts
Tomatoes
Consumers 4
5
3
6
Retailers
7
8
4
4
Wholesalers 2
4 0 1
Page 1 of 4

In order to sell the produce in these towns the society pays a commission to salesmen, town mangers
and d division managers as shown below
Salesman Towns
Division
Manager Manager
Nakuru

6%
5%

2%
Mombasa

4%
3%
3%

The selling price per bag sis given as follows

Selling price per bag (Kshs)
Maize

200
Potatoes

1,000
Carrots

500
Tomatoes

700

Using matrix algebra:
a)
Find total sales in units by product and customer type

( 4 marks)
b)
Determine the difference between the two towns in sale s( in units) by product and

customer type

( 4 marks)
c)
Calculate the total sales in shillings by each town

( 8 Marks)
d)
Find sales in shillings by customer type for each town

( 8 Marks)
e)
Compute the amount of commission to be paid by type of commission and type of

customer

( 6 Marks)

Page 2 of 4

Question 2
Using examples explain the meaning of the following terms used in hypothesis testing:-
a)
Simple and Composite hypothesis

( 2 marks)
b)
Null and Alternative Hypothesis

( 2marks)
c)
Acceptance and rejection regions

(2 marks)
d)
One tailed and two tailed tests

(2 marks)
e)
Type I and type II errors

(2 marks)

Question 3
The main daily Newspaper in Nyeka are: The National, the New Era and The Citizen. The
management of one of the dailies is concerned d about the low sales volume of their paper. In a
recent survey of 100 families in Yairobi, the numbers (hypothetical) that read the various newspapers
were found to be as follows:
Newspaper

Number of readers
The Citizen

28
Citizen and New Era

8
The New Era

30
Citizen and National

10
The National

42
New Era and national

5
All the three papers

3

a)
Determine the number of families who did not read any of the three newspapers ( 4 Marks)
b)
Mrembo Beauty advertising firm in Yairobi wants to know which newspaper they should

advertise in so that they can reach the largest audience. Advise the company.
( 2 Marks)
c)
Discuss the use of Venn diagram in the set theory. Illustrate your answer.
( 4 Marks)

Page 3 of 4

Question 4
Paul Kirabi, a Senior Accountant with the Bluenile group of companies has obtained estimates in
relation to the production of its flagship product. The weekly costs of production, C, are given by the
equation:
C=100+23x+ 0.5x2
Where X is the number of tones produced. The weekly revenue equation, R , is givem by

R=100x- x2 (x<100)

You are required to:
a)
Find the production level(s) at which profit is maximized

( 4 Marks)
b)
Find any break-even point(s)

( 3 Marks)
c)
Find the point at which revenue would be maximized

( 3 Marks)

Question 5
Madallas ltd is a furniture workshop that makes chairs and stools in Kisumu. The following statistics
were provided by the accountant of the business.
To make 80 stools and 50 Chairs they will spend shs 8,000 on labour and shs 6,000 on materials. In
order to make 30 stools and 70 Chairs they will spend shs 4,300 on labour and shs 3,000 on
materials. The shop makes a profit of 30% and 40 % on each stool and chair respectively.
a)
Express the above cost of making a stool and a chair in the form a simultaneous equation

( 4marks)
b)
Calculate the cost of making a stool and a chair

( 4 marks)
c)
What are the selling prices for a stool and a chair

( 2 marks)

Question 6
a)
Describe the conditions that must be satisfied for linear programming to be useful

in solving optimization problems

( 5 Marks)
b)
Discuss the limitations of linear programming as a mathematical technique
(5 Marks)
********************

Bme 500: Quantitative Methods For Managers Question Paper

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