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Bcom 272: Operations Research I Question Paper
Bcom 272: Operations Research I
Course:Bachelor Of Commerce
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
SECOND YEAR EXAMINATIONS FOR THE AWARD OF DEGREE IN BACHELOR OF COMMERCE
BCOM 272: OPERATIONS RESEARCH I
STREAMS: BCOM Y2S2 TIME: 2 HOURS
DAY/DATE: WEDNESDAY 17/4/2013 2.30 PM – 4.30 PM
INSTRUCTIONS:
1. (a) Operations research is a scientific and systematic approach in decision making
which involves several steps. Discuss the steps. [7 Marks]
(b) Discuss the contribution that operations Research can make in the Kenyan economy in achieving vision 2030. [7 Marks]
(c) Operations research extensively uses models in problem solving. Highlight any
five advantages in using models in decision making. [7 Marks]
(d) Five different machines can do any of the five required jobs with different profits
resulting from each assignment as follows:
Job Machines
A B C D E
1 30 37 40 258 40
2 40 24 27 21 36
3 40 32 33 30 35
4 25 38 40 36 36
5 29 62 41 34 39
Required:
Determine the maximum profit possible through optimum assignments. [9 Marks]
2. (a) Discuss the term degeneracy as used in simple method of linear programming.
[3 Marks]
(b) A company produces three products A, B, and C. The unit profit contribution of each of the products are Ksh. 5, 10 and 8 respectively. Each unit of product A requires 3kgs of material, 4 machine hours and 2 labour hours; each units of product B requires 5kgs of material, 4 machine hours and 4 labour hours; each unit of product C requires 2kgs of material, 4 machine hours and 5 labour hours. The company has 60 kgs of materials, 72 machine hours and 100 labour hours available everyday. The company want to maximize its daily profits using the available resources,
Required:
(i) Formulate the above problem as a linear programming model.
[5 Marks]
(ii) Write the problem in (i) above in its tableau form. [4 Marks]
(iii) Draw the initial simplex tableau and show
(a) The entering variable
(b) The leaving variable
(c) The pivot element. [5 Marks]
(c) State any three advantages of the simplex method. [3 Marks]
3. A project consists of the following activities with their times in days;
Activity Preceding Activity Optimists time Pessimists time Most likely time Total time
A - 1 5 1.5 7.5
B A 1 3 2 6
C A 1 5 3 9
D B 3 5 4 12
E B, C 2 4 3 9
F B, C 3 7 5 15
G D, E 4 6 5 15
H F 6 8 7 21
I G, H 2 6 4 12
J G, H 5 7 6 18
K I 1 3 2 6
L J 3 7 5 15
Required:
(i) Draw a PERT diagram for the project. [6 Marks]
(ii) Determine the critical path and project duration. [4 Marks]
(iii) If a 30 day deadline has been imposed, what is the probability of completing the project on time. [4 Marks]
(iv) What is the probability of completing the project before 25 days? [6 Marks]
4. (a) The following data relates to compound k10.
Maximum monthly usage 300 units
Minimum Monthly usage 200 units
Lead time maximum 6 months
Lead time minimum 2 months
Reorder quantity 750 units
Calculate the Reorder level, minimum stock and average stock.
[7 Marks]
(b) Using suitable example, explain and differentiate between pure strategy
and mixed strategy games. [4 Marks]
(c) Using suitable examples, distinguish between cooperative and non
cooperative games. [4 Marks]
(d) State any five benefits of inventory control to an organization.
[5 Marks]
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