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Operation Research One Question Paper
Operation Research One
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2010
UNIVERSITY EXAMINATIONS: 2009/2010
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
CMS 201: OPERATION RESEARCH ONE (day + evening)
DATE: AUGUST 2010 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
a) Develop a flow chart for solving a linear programming problem using simplex algorithm
approach. (10 Marks)
b) What is the meaning of the following terminologies used in operations research?
i. Surplus Variable. (1 Mark)
ii. Slack Variable (1 Mark)
iii. Opportunity Cost (1 Mark)
iv. Utilisation factor (1 Mark)
v. Free Float (1 Mark)
c) A management student identifies the following list of activities and sequencing requirements along
with the time estimates for variable activities related to the completion of his project work.
Activity times (in days)
Activity list
Immediate
predecessors Optimistic
(a)
Most
likely (m)
Pessimistic
(b)
A Search of list - 3 6 9
B Deciding the project - 2 4 12
C Preliminary work B 1 1.5 5
D Formal proposal C 1 2 3
E Project committees approval A, D 1.5 3 4.5
F Progress report E 0.5 1 1.5
G Formal research A, D 4.5 5 11.5
2
H Data collection E 2 5 8
I Analysis G, H 4 5.5 10
J Conclusion I 1.5 1.5 4.5
K Draft I, F 2 3.5 8
L Final draft J, K 2.5 3 3.5
M Presentation L 0.5 1 1.5
Required:
i. Draw a network diagram to determine the minimum time required to complete the project.
ii. What is the probability of completing project within 30 days? (15 Marks)
QUESTION TWO
a) Distinguish between the following:
(i) Transportation problem and Assignment problem.
(ii) Stepping Stone method and Modified Distribution method. (5 Marks)
b) URIRI Chemicals Ltd., are producing their main product in their three factories that are allocated at
Awendo, Rapogi and Migori. The product is sold through four distributors who are again located
at different places. They are Nyarago Chemical, PVT Ltd (NCPL) Nyamasare Chemical Agency,
(NCA), Chunge Chemical, Distributors (CCD) and Bware Chemicals & Co. (BCC). The costs in
shillings of product per unit and the capacity of each factory in unit is given below:
Factory Cost in (Shs) per unit Capacity in units
Awendo (A) 12 200
Rapogi (R) 13 300
Migori (M) 11 100
The sale price at which the product is sold to distributors are given below:
Distributors Selling price (Shs) per unit Demand (in units)
NCPL 16 150
NCA 17 250
CCD 15 100
BCC 19 200
The distribution cost per unit (Shs.) from a factory to distributor is given in the following
matrix.
3
FACTORY NCPL NCA CCD BCC
Awendo (A) 1.0 1.1 1.2 1.5
Rapogi (R) 2.1 2.0 1.5 3.0
Migori (M) 1.8 1.5 1.1 1.6
Required:
Find an optimal distribution programme for the company. (15 Marks)
QUESTION THREE
a) Nyamasaria Computer’s Innovators Ltd. (NCI) would like to provide a computer programming
solutions for solving assignment problem. You have been identified as a key advisor with the task
of assisting the developers in understanding the solution procedure for solving assignment
problem.
Required:
Generate a flow chart for solving assignment problem based on Hungarian approach. (10 Marks)
b) In a textile sales emporium four salesmen A, B, C and D are available to four counters W, X, Y and
Z. Each salesman can handle any counter. The service (in hour) of each counter when manned by
each salesman is given below:
SALESMEN
A B C D
W 41 72 39 52
X 22 29 49 65
Y 27 39 60 51
Z 45 50 48 52
Required:
How should the salesmen be allocated appropriate counters so as to minimize service time?
(Each salesman must handle only one counter). (10 Marks)
QUESTION FOUR
a) In situations, where mathematical simplification is not feasible, simulation is an important
substitute for mathematical evaluation of a model.
Required:
4
Discuss the reasons for adopting simulation in place of other known mathematical techniques.
(5 Marks)
b) Bayer Pharmaceutical produces three kinds of cold formulas. Formula I, formula II and formula
III. It takes 2.5 hours to produce 1,000 bottles of formula I, 3 hours to produce 1,000 bottles of
formula II and 4 hours to produce 1,000 bottles of formula III. The profits for each 1,000 bottles of
formula I, formula II and formula III are Sh.180, Sh.200, and Sh.300 respectively. Suppose that
for a certain production run there are enough ingredients on hand to make at most 9,000 bottles of
formula I, 12,000 bottles of formula II and 6,000 bottles of formula III. Furthermore, suppose that
the time for the production run is limited to a maximum of 70 hours.
Required:
Find how many bottles of each formula should be produced in this production run so that the
profit is maximized? (15 Marks)
QUESTION FIVE
a) The effort of AK Erlang in 1909 to analyse telephone traffic congestion with the objective of
meeting uncertain demand for service at the Copenhagen telephone system which resulted in a new
theory (queuing or waiting line theory) is a valuable tool in business because many business
problems can be characterized as arrival-departure congestion problems.
Required:
Discuss the above statement identifying where queuing theory have been applied, what are some of the
limitation of queuing theory (5 Marks)
b) M-NET Studi Barber shop is a popular haircutting saloon near the KCA University Ruaraka
Campus. Four barbers work full time and spend an average of 15 minutes on each customer.
Customers arrive all day long at an average rate of 12 per hour. Arrivals tend to follow the Poisson
distribution, while service times are exponentially distributed.
Required:
i. What is the probability that the shop is empty? (3 Marks)
ii. What is the average number of customers in the barber shop? (3 Marks)
iii. What is the average time spent in the shop? (3 Marks)
iv. What is the average time that a customer spends waiting to be called to the barber chair?
(3 Marks)
v. What is the average number waiting to be served? (3 Marks)
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