This document contains an exam for a Bachelor of Commerce degree in Operations Research. It includes 5 questions testing various concepts in operations research. Question 1 has parts on inventory reasons, queuing arrivals, and formulating a linear programming problem. Question 2 involves multiple decision criteria for an advertising program choice. Question 3 covers holding costs and an economic order quantity problem. Question 4 tests project management phases and performing a critical path analysis. Question 5 has parts on queuing behavior factors and analyzing a healthcare queuing system.

1. Exam Name: Bcom 272: Operations Research I
Course: Second Year Examination For The Award Of The Degree Of Bachelor Of Commerce
Institution/Board: Egerton University
Exam Year:2011
INSTRUCTIONS:
Attempt Question ONE and any other TWO Questions.
QUESTION ONE
a) Inventory makes up a large proportion of current assets in an organization, sometimes up to
60%. Explain FIVE reasons organizations insist on keeping inventory. (10 marks)
b) Describe the THREE types of arrivals regarded in the queuing system. Provide a relevant
example for each case. (6 marks)
c) The Operations Manager of a petroleum oil refinery must decide on the optimal mix of two
possible blending processes. The inputs and outputs per production run are represented in the
table below:-
Process Input Output
Grades A: B: Petroleum m2
X X Y
1 5 3 5 8
2 4 5 4 4
The maximum amounts available of crude A and B are 200 units and 150 units respectively.
Market requirements show that at least 100 units of Petroleum X and 80 units of petroleum Y
must be produced. The profits for production run from process 1 and 2 are Kshs. 3 and Kshs. 5
respectively.
Required
i) Formulate the above problem as a LP model. (6 marks)
ii) Solve (i) above using the appropriate technique. (4 marks)
d) Explain FOUR problems encountered when applying operations Research Techniques. (8
marks)
QUESTION TWO
The manager of an advertising agency has to make a decision between three available programs
(a1, a2, a3). There are three possible futures that can be expected: S1 = market rises, s2 =market
falls, S3 =no change in the market. The manager can estimate the yields in each case as given in
the table below in percentage of return; however the manager cannot estimate the probabilities of
the various future occurring:-
Programs/ futures S1 S2 S3
A1 3 6 -1

2. A2 8 5 4
A3 -4 7 12
Required:-
Determine which program you would advise the manager to select the following decision
approaches:-
i) Laplace (4 marks)
ii) Pessimistic (4 marks)
iii) Optimistic (4 marks)
iv) Hurwitz criterion with =.55 (4 marks)
v) Mini max regret (4 marks)
QUESTION THREE
a) Describe FOUR variables holding costs. (8 marks)
b) A publication concern uses 2,500 packets of paper each year. The ordering cost is Kshs.24 per
order. Storage and interest costs have been estimated at Kshs.2.50 per packet per annum based
on the average annual stock. The price per packet is Kshs. 18. The usual supplier has offered a
5% quantity discount if the printer purchases 800 or more packets at any one time.
Required:
Advise the printer whether to take the offer or not. (Show your workings clearly) (12 marks)
QUESTION FOUR
a) Explain FIVE concern of any management in projects management. (5 marks)
b) Make short notes on the following project phases which facilitate project analysis.
i) Planning phase (2 marks)
ii) Scheduling phase (2 marks)
iii) Control phase (2 marks)
c) Banyamulenge contractors have come up with the following project data:
Activity Duration (days)
1-2 8
1-3 10
1-11 20
2-8 5
3-7 6
3-8 8
7-8 1
7-11 10
8-11 -
Required:
i) Draw the network diagram for the contractors. (4 marks)
ii) Determine the critical path. (4 marks)

3. iii) Determine the project’s duration. (1 mark)
QUESTION FIVE
a) Describe SIX behavior factors which help facilitate queuing decision. (Give an appropriate
example for each case) (6 marks)
b) In a newly established health center, Metropolis Health Center, there is a single medical
doctor who takes care of patients arriving. The management is convinced that the situation faced
by the doctor is a single server queuing situation with Poisson arrivals and poison service. It has
been established over time that patients arrive randomly at a rate of 0.20 patients per hour. Each
patient requires different amount of time for treatment. However, the doctor reckons that he
treats his patients at an average of 0.25 patients per hour.
Required: - Determine:
i) The average number of patients in the queuing system. (2 marks)
ii) The number of patients actually waiting in the queue. (2 marks)
iii) The average amount of time a patient spends in the queue system. (2 marks)
iv) The average amount of time a patient spends in the queue. (2 marks)
v) The probability of having exactly FIVE patients in the queuing system (2 marks)
vi) The probability that there will be fifteen or more patients in the queuing system (2 marks)
vii) The utilization ratio with the doctor functioning as the service mechanism. (2 marks)