# Kenya Methodist University

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```					                             siKenya Methodist University
School of Business Studies & Management

lecturer         :      Wilson Muema

Instructions

1. Answer All Questions in section A and Two question in Section B
2. ASSIGNMENTS ARE DUE BEFORE 5TH JULY, 2011
4. 20 MARKS WILL BE SUBTRACTED IF SUBMITTED AFTER DEADLINE
5. Plagiarism is a serious academic offence
6. Reference your work using APA style
7. YOU ARE ADVISED TO READ EXTENSIVELY ON THE TOPICS INDICATED ON

SECTION A

Question One
a) Discuss the assumptions of linear regression

b) Which average would be more suitable in the following cases? Give reasons

ii.   Average intelligence of students in a class

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iii.     Average production per shift in a factory

iv.      Average rate of growth of population per decade

c)        The median and mode of the following wage distribution are known to be £33.5 and
£34 respectively. Three frequency values from the table are however missing.

Wages ( in £.)                          No. of workers
0-10                                              4
10-20                                             16
20-30                                             ?
30-40                                             ?
40-50                                             ?
50-60                                             6
60-70                                             4
Total                                             230

Required:
i)            Find the missing values                                      8 marks
ii)           Compute the mean                                             3 marks
iii)          Compute standard deviation                                   4 marks
iv)           Comment on the distribution of wage                          2 marks
c) Particulars regarding the income of two villages are given below.

Village X            Village Y
Number of people                             600        500
Average income ( in £)                       175        186
Variance of income ( in £)                   100        81

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i) in which village is the variation in income greater?
ii) what is the combined standard deviation of the village X and village Y put together?
What inference can you make from this?

d) Consider an emergency room of a small rural hospital where the past records indicate an
average of 5 arrivals daily. The demand for emergency room service at this hospital is
distributed according to a Poisson distribution. Calculate the probability of exactly 0, 1,
2 and 3 arrivals. What is the probability of more than 2 arrivals?
e) Discuss the assumptions of linear programming.
f) Highlight the assumptions of Linear Multiple Regression Analysis
g) Determine the multiple linear regression equation of X1 on X2 and X3 from the data
relating to three variables given below. Use the regression equation to compute the value
of X1 when X3 is 22

X1 4        6       7      9      13       15
X2 15       12      8      6      4        3
X3 30       24      20     14     10       4

h) Describe the properties of normal distribution
i) A sample of 100 dry cells tested to find the length of life produced the following results:
Mean=12 hours                    standard deviation = 3 hours
Assuming the data to be normally distributed, what percentage of battery cells are
expected to have life :
i.   More than 15 hours
ii.    Less than 6 hours
iii.   Between 10 and 14 hours
j) Describe the term game theory and describe at least three types of games.

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k) Reduce the following game by Dominance and find the game value.

TABLE 1

PLAYER B
I       II                III          IV
I         3   2                 4         0
PLAYER A                     II        3   4                 2         4
III       4   2                 4         0
IV        0   4                 0         8

Question Two
l) At a particular Automatic Teller Machine (ATM), customer’s arrival follows a Poisson
distribution with an average time of 6 minutes between arrivals. The time- intervals
between services at ATM is 3 minutes. On the basis of this information, answer the
following questions:
i)         What would be the expected average queue length?

ii)        What would be the average number of customers in the queuing system?
iii)       How long on average does a customer have to wait in the queue?

iv)        How much time on average does a customer spend in the system?
Question three
a) Describe the following terms as used in network analysis
i.   Critical activity
ii.   Super critical activity
iii.      Float
iv.       Sub-critical activity
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b) R&D department is planning to bid on a large project for the development of a new
communication system for commercial planes. The accompanying table shows the activities,
times and sequences.

Activity          Preceding      Time in Days
Activity       Optimistic             Most likely        Pessimistic
Time                       Time               Time
A                 -              6                             6               24
B                 -              6                            12               18
C                 -              12                           12               30
D                 A              6                             6                6
E                 B              12                           30               48
F                 C              12                           30               42
G                 D,E            18                           30               54
H                 B              17                           29               47
I                 H,F            14                           28               48
J                 G,I            14                           28               48
K                 J              6                             6               24

Required:-
a) Draw a network to represent the above data
b) Determine the critical path of the project and the expected project length
c) Calculate the variance and standard deviation of the project
d) Compute the probability of completing the project within a period of 120 days
e) Suppose you want to shorten the completion time as much as possible and have the option of
shortening any or all of B, C, D and G each by two days. Which would you shorten? What
would be the new critical path?

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SECTION B

Question One
a) Describe the limitations of linear programming technique.
b) XYZ Company ltd has two bottling plants, one located at Mombasa and the other at Voi.
Each plant produces three drinks, A, B and C. The number of bottles produced per day are
as follows:

PLANT AT
Mombassa        Voi
(M)         (V)
Drink A               1500            1500
Drink B               3000            1000
Drink C               2000            5000
A market survey indicates that during the month of December 2010, there will be a demand of
20000 bottles of A, 40000 bottles of B and 44000 bottles of C. The operating costs per day for
plants at Mombassa and Voi are 600 and 400 monetary units respectively. For how many days
should each plant be run in the month of December so as to minimize the production cost, while still
meeting the market demand?

Question Two
a) Highlight the assumptions in a transportation model.
b) Describe the following terms as used in transportation problems
i.   Feasible solution
ii.   Basic feasible solution
iii.   Optimal solution
c) A product is produced by four factories, A, B, C and D. The unit production costs in them
are £2, £3,£1 and £5 respectively. Their production capacities are are: factory A- 50 units,
B-70 units, C- 30 units and D- 50 units. These factories supply the product to four stores
whose demands are 25, 35, 105 and 20 units respectively. Unit transport cost in rupees from
each factory to each store are given in table 2 below

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TABLE 2

STORES
1          2               3                4
A             2             4                6               11
B             10            8                7               5
Factories
C             13            3                9               12
D             4             6                8               3

Required:
Determine the extent of deliveries from each of the factories to each of the stores so that
the total production and transportation cost is minimum
Question three
a) Describe the term simulation
c) Meru bakery keeps stock of a popular brand of cake. Daily demand based on past experience
is given below:

Daily demand:              0       15     25         35       45          50
Probability:               0.01    0.15   0.20       0.50     0.12        0.02
Consider the following sequence of random numbers:
48       78        09      51     56         77       15          14     68   09
i.   Using the sequence, simulate the demand for the next 10 days
ii.   Find the stock demand if the owner of the bakery decides to make 35 cakes every day. Also
estimate the daily average demand for the cakes on the basis of the simulated data.

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Question four
You are given the position in a factory before and after the settlement of an industrial dispute.
Comment on the gains or losses from the point of view of workers and that of management.

Before                         After
No. of workers                                2400                           2350
Mean wages ( in 000 Kshs)                     45.5                           47.5
Median wage ( in 000 ksh)                     48.0                           45.0
Standard deviation(ksh)                       12.0                           10.0

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