Operations Research 1 Question Paper

Operations Research 1

Course:Bachelor Of Arts In Economics And Statistics

Institution: Kenyatta University question papers

Exam Year:2009

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
ARTS AND BACHELOR OF EDUCATION

AEC304: OPERATIONS RESEARCH 1

DATE: Thursday, 24th December, 2009 TIME:: 4.30 p.m. ? 6.30 p.m.

INSTRUCTIONS
Answer Question One and any other two questions.
Question One (Compulsory)
A firm produces three products X1, X2 and X3. It uses two resources; man hours and raw
materials.
? To produce a unit of X1, the firm requires 6 hours and 2 units of raw
materials.
? To produce a unit of X2, the firm requires 3 hours and 2 units of raw
materials.
? To produce a unit of X3, the firm requires 5 hours and 10 units of raw
materials.

Only 30 man hours and 50 units of raw materials are available. If profits per unit of
product X1, X2 and X3 are 30, 24 and 60 respectively;

a) Formulate the linear programming problem for the firm and solve for the optional
solution. (15 Marks)
b) Interpret the above solution as thoroughly as possible. Be sure to interpret the
shadow prices/marginal values for the resources.
(5 Marks)
c) Formulate the dual problem corresponding to the problem in (a) above. Using the
dual theorems, determine the optimal solution to the dual problem.

(10 Marks)
Question Two
2. A company has four factories F1, F2, F3 and F4 manufacturing the same product.
Production and raw material costs differ from factory, and are given in the
Page 1 of 4
following table in the first two rows. The transportation costs from the factories
to sales deports S1, S2, S3 are also given.
The last two columns in the table give the sales price and the total requirement at
each depot. The production capacity of each factory is given in the last row.

F1 F2 F3 F4 Sales
Requirements

Price
in

Per
Units
Production cost/unit
15
18
14
13

Raw material cost/unit
10
9
12
9

S1
3
9
5
4
34
160
Transportation S2
1
7
4
5
32
240
Cost per Unit: S3
5
8
3
6
31
300

20 300 100 400

Determine the most profitable production and distribution schedule and the
corresponding profit. (Hint: Obtain the schedule that minimizes transportation costs first)

(20 Marks)

Question Three
Tulsian Company has five plants each of which can manufacture any one of five
products. Production costs differ from one plant to another as do sales revenue. Given
the revenue and cost data below, obtain which product each plant should produce to
maximize profit. What will be the maximum profit?

Sales Revenue (K.sh?000) Production Cost (K.sh?000.)
Product Product
Plant 1 2 3 4 5 Plant 1 2 3 4 5
A 65 78 83 60 95
33 40 43 32 45
B 85 52 59 44 73
45 28 31 23 37
C 83 56 69 64 78
42 29 36 29 41
D 49 80 85 84 73
27 42 44 38 37
E 59 68 83 74 83
30 35 43 39 44
(20 Marks)
Question Four
Four months ago, a Restoration team submitted a competitive bid to the Lake Basin
Authority to revitalize Lake Victoria in Western Kenya. The team had developed a new
technique to combat water pollution by increasing the basic amount of oxygen in a
lake, called oxygenation.

Oxygenation of a lake is a very complex project involving specialized equipment and
specially trained personnel. The contract was for a period of more that half of a year, a
long enough period for significant changes to occur in the economy and in the availability
of resources. The Authority wanted the project to be completed on time and therefore the
contract contained a $2000 token clause for each week below the agreed ? on 30-week
completion time.
Page 2 of 4

The team felt that planning, monitoring and controlling this job could be staggering.
The team approaches you having done a course in operations management. After
consulting with the team, you came up with a list of activities with each activity clearly
defined as below:

Activity Activity Description
Duration in Weeks Preceding
Activities
a
Administrative Set-up
3
-
b
Hire Personnel
4
a
c
Obtain materials
4
a
d
Transport materials to the lake
2
c
e
Gather measuring team
4
a
f
Planning
6
c
g
Assemble equipment
3
d,b
h
Plan evaluation
1
e
I
Oxygenation
12
f,g
j
Measurement & Evaluation
2
i,h

Required:
(a)
Briefly explain three main functions in project management(3 marks)

(b)
Set up the project network showing the various activities and durations.
(10 marks)
(c)
Determine the critical path hence the critical activities of the project.
(3 marks)
(d)
What is the longest period that the project can take to complete?
(1 mark)
(d)
After completing the project, the Lake Basin Authority did not honor the
token clause and hence the Restoration Team sued the Authority for
breach of contract. How much would the Authority have to pay to the
team if the case is in favour of the team?

(3 marks)

Question Five
a) Two candidates PNU and ODM are competing for the councilor?s seat in a City
Municipal council, and PNU is attempting to increase his total votes at the
expense of ODM. The strategies available to each candidate involve personal
contacts, newspaper insertions/speeches or television appearance/advertising.
The increase in votes available to PNU given various combination of strategies
are given below:-

Page 3 of 4
ODM

Personal Contacts
Newspapers
T.V.
PNU
Personal 30,000 20,000 10,000
Contacts
Newspapers
60,000
50,000
40,000
T.V.
20,000
40,000
30,000

(i)
Define a saddle point(2 Marks)
(ii)
Determine the optimal strategies that should be adopted by PNU, during his
election campaign. (5 Marks)
(iii)
How many votes should PNU gain by following the optimal strategy? (1
Marks)

b) M/s Kiti pharmaceuticals is currently involved in negotiations with its union on the
upcoming wage contract. A consultant informs the management group that he has
been in touch with the executive members of the union and they have constructed a
table that is comparable to the pay-off matrix developed by the management. With
the help of the management consultant, who specializes in industrial relations, the
following pay-off matrix was constructed by the management of the company. A
positive pay-off indicates a wage increase. Both the management and the union must
decide on an overall strategy before the commencement of negotiations.

Union strategies

U1
U2
U3
U4
Management C1 -0.35 -0.35 -0.45 -0.12
Strategies C2 0.30
0.26
-0.18
-0.18

C3 0.24
0.22
-0.25
-0.23

C4
0.40
-0.20
-0.24
0

What strategies are available to the opposing groups and what is the outcome? (12
Marks)

Page 4 of 4

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