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Cms 201 Operations Research Question Paper
Cms 201 Operations Research
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2011
UNIVERSITY EXAMINATIONS: 2011/2012
YEAR 3 EXAMINATION FOR THE BACHELOR OF COMMERCE
CMS 201 OPERATIONS RESEARCH I (Day & Eve)
DATE: APRIL 2012 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One and Any other Two Questions
QUESTION ONE
Consider a project having the following activities and their time estimates
Activity Immediate
Predecessor
most optimistic most likely most pessimistic
A - 3 4 5
B - 4 8 10
C B 5 6 8
D A,C 9 10 15
E B 4 6 8
F D,E 3 4 5
G D,E 5 6 8
H D,E 1 3 4
I G 2 4 5
J F,I 7 8 10
K G 4 5 6
L H 8 9 13
M J,K,L 6 7 8
Required
(a) Draw a network diagram for the project [10 Marks]
(b) Compute the expected project completion time [5 Marks]
2
(c) What should be the due date to have 0.80 probability of completion [5 Marks]
(d) Calculate the Total and Free float for all non-critical activities. [10 Marks]
[Total 30 Marks]
QUESTION TWO
Six salesmen are to be allocated to six sales regions so that the cost of the allocation of the job will be
minimum. Each salesman is capable of doing the job at different costs in each region. The cost in
thousands of shillings matrix is given below
Regions Salesmen
I II III IV V VI
A 15 35 0 25 10 45
B 40 5 45 20 15 20
C 25 60 10 65 25 10
D 25 20 35 10 25 60
E 30 70 40 5 40 50
F 10 25 30 40 50 15
Required
a) Allocate the salesmen to the sales region to minimize the cost [15 Marks]
b) What is the minimum cost [5 Marks]
[Total 20 Marks]
QUESTION THREE
A manufacturer has distribution Centres at X, Y and Z. These centres have the availability of 40, 20
and 40 units of his product. His retail outlets at A, B, C, D and E require 25,10,20,30 and 15 units
respectively
Distribution
Centres
Retail outlets
A B C D E
X 55 30 40 50 40
Y 35 30 100 45 60
Z 40 60 95 35 30
Required
3
(a) Develop a linear programming problem (Do not solve) [5 Marks]
(b) Determine the initial solution to minimise the cost of transportation [5 Marks]
(c) Determine the optimal distribution to minimise the cost of transportation [10 Marks]
[Total 20 Marks]
QUESTION FOUR
Bright Bakery keeps stock of a popular brand of cake. Previous experience indicates the daily demand
as given here:
Daily Demand: 0 10 20 30 40 50
Probability: 0.01 0.20 0.15 0.30 0.32 0.02
Consider the following sequence of random numbers:
Random Number: 48,78,19,51,56,77,15,14,68,09.
Using this sequence, simulate the demand for the next 10 days. Find out the stock situation, if the
owner of the bakery decides to make 30 cakes per day. Also estimate the daily demand for the cake on
the basis of simulated data.
[Total 20 Marks]
QUESTION FIVE
DONIX Consulting specialises in two types of consultancy project.
• Each type A project requires twenty hours of work from qualified researchers and eight hours of
work from junior researchers.
• Each type B project requires twelve hours of work from qualified researchers and fifteen hours
work from junior researchers.
Researchers are paid on an hourly basis at the following rates:
Qualified researchers Sh$30/hour
Junior researchers’ Sh14/hour
Other data relating to the project:
Project type
A B
Sh Sh
Revenue per project 1700 1500
Direct project expenses 408 310
Administration 280 270
4
*Administration costs are attributed to projects using a rate per project hour. Total administration costs
are $28,000 per four week period.
During the four week period ending on 30th June 20x0, owing to holidays and other staffing difficulties
the numbers of working hours available are:
Qualified researchers 1344
Junior researchers 1120
An agreement has already been made for twenty type A projects with XYZ group. RAB consulting
must start and complete these projects in the four week period ending 30th June 20x0.
A maximum of 60 type B projects may be undertaken during the four week period ending 30th June
20x0.
DONIX consulting is preparing its detailed budget for the four week period ending 30th June 20x0 and
needs to identify the most profitable use of the resources it has available.
Required
a) Calculate the contribution from each type of project. [ 5 Marks]
b) Determine the optimal production plan for the four week period ending 30th June 20x0, assuming
that DONIX is seeking to maximise the profit earned. [3 Marks]
c) You should use a linear programming graph, identify the feasible region and the optimal point
and accurately calculate the maximum profit that could be earned using whichever equations
you need. [10 Marks]
d) Explain the meaning of a shadow price and calculate the shadow price of qualified researcher
time. [ 2 Marks]
[Total 20 Marks]
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