Get premium membership and access revision papers, questions with answers as well as video lessons.
Operation Reasearch I Question Paper
Operation Reasearch I
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2011
UNIVERSITY EXAMINATIONS: 2010/2011
THIRD YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
CMS 201: OPERATION REASEARCH I
DATE: AUGUST 2011 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
Question One
a) SUMERCI DISTSRIBUTORS has four manufacturing plants and five warehouses .Each plant
manufactures the same product which is sold at different prices at each warehouse area. The cost of
manufacturing and cost of raw materials are different in each plant due to various factors .The
capacities of the plants are also different. The data are given in the following table
Items plants
1 2 3 4
Manufacturing
cost/unit
12 10 8 8
Raw Material
cost/unit
8 7 7 5
Capacity per
unit time
100 200 120 80
The company has five warehouses .The sales prices, transportation costs, and demand are given in the
following table
2
Warehouses Transportation cost per unit
1 2 3 4
sales price
per unit
demand
A 4 7 4 3 30 80
B 8 9 7 8 32 120
C 2 7 6 10 28 150
D 10 7 5 8 34 70
E 2 5 8 9 30 90
Required
i) Formulate this problem into transportation problem to maximise profit [5 Marks]
ii) Find the solution using VAM [8 Marks]
iii)Test for optimality and find the optimal solution [9 Marks]
b) Differentiate the following concepts as used in operations research
i) Critical path method (CPM)and project evaluation and review technique(PERT) [2 Marks]
ii)Transportation problem and assignment problem [2 Marks]
iii) Degeneracy in transportation problem and degeneracy in linear programming problem
[2 Marks]
iv) Waiting cost and service cost as used in queuing theory [2 Marks]
[Total: 30 Marks]
Question Two
a) Explain the difference between Least Cost Method (LCM) and North West Corner (NWC) rule as
used in assignment models. [5 Marks]
b) DONIX HOLDINGS marketing manager has five salesmen and five sales districts. Considering the
capabilities of the salesmen and nature of districts, the marketing manager estimates that sales per
month (in thousands of shillings ) for each salesman in each district would be as follows
Districts
Salesmen A B C D E
1 32 38 40 28 40
2 40 24 28 21 36
3 41 27 33 30 37
4 22 38 41 36 36
5 29 33 40 35 39
3
Required
Find the assignment of salesmen to districts that will result in maximum sales [15 Marks]
[Total: 20 Marks]
Question Three
K.K Limited manufactures security systems for homes. To enable the company offer a better quality
product at a lower cost than its competitors, the company has decided to expand its present facility to
accommodate a new line. A project team has been formed within the company to direct and coordinate
the plant expansion.
This team met weekly to monitor the status of the project.
Prior to the start of the plant expansion, the management developed the following list of required
activitie
Activity Normal Crash
Predecesso
r
Time
in
weeks
Costs
(Sh)
‘000’
Time
in
weeks
Cost
(Sh)
‘000’
A Prepare architectural
plan
- 10 10,000 7 12,000
B Construct building A 35 50,000 33 52,000
C Develop equipment
Specifications A 4 7,000 3 6,000
D Design and construct
Equipment C 25 20,000 25 26,000
E Install/Test equipment B,D 5 5,000 4 4,500
F Develop staffing plan C 2 4,000 2 4,000
G Hire staff F 4 30,000 2 30,000
H Train staff G 2 15,000 1 25,000
I Pilot production run E,H, L 1 4,000 1 4,000
J Market research - 8 12,000 4 24,000
K Complete product
development - 12 24,000 10 20,000
L Complete package
design J,K 4 6,000 2 2,000
M Complete marketing
plan J 8 10,000 6 8,000
4
Required:
a) Determine the critical path and list the critical activities. [8 Marks]
b) Determine the minimum time and minimum cost network. [7 Marks]
c) K. K Ltd knows that other companies are working on a competing product. The company estimates
that the delay of every week beyond the 40th week in bringing out the new line will cost the firm
sh. 1,000,000 in lost profit..
d) What will be the cost to the firm if the project is completed in 50 weeks? [3 Marks]
e) Is it advisable to crash the profits from 51 to 45 weeks? Why? [2 Marks]
[Total:20 Marks]
Question Four
(a)The simplex table for a maximisation problem of a linear programming is given here
cj 4 5 0 0
xj x1 x2 s1 s2 quantity
(bi)
5 x2 1 1 1 0 10
0 s2 1 0 -1 1 3
zj 5 5 5 0 50
cj-zj -1 0 -5 0
Required
i) Is this solution optimal [2 Marks]
ii) Are there more than one optimal solution [1 Mark]
iii)is this solution degenerate [1 Mark]
iv)is this solution feasible [1 Mark]
v) if S1 is slack in machine A(in hours /week) and s2 is slack in machine B (in hours/week),which of
these machines is being used to full capacity when producing according to this solution [1 Mark]
vi)A customer would like to have one unit of product x1 and is willing to pay in excess of the normal
price in order to get it .how much should the price be increased in order to ensure no reduction in
profits? [1 Mark]
vii)How many units of the two products x1 and x2 are being produced according to this solution and
what is the total profit? [1 Mark]
viii) Machine A (associated with slack s1, in hours per week) has to be shut down for repairs for 2
hours next week. What will be the effect on profits? [1 Mark]
5
ix)How much would you be prepared to pay for another hour (per week) of capacity each on machine
A and Machine B? [1 Mark]
(b)At a service counter of STAR CODE FOODS, the customers arrive at the average interval of six
minutes whereas the counter clerk takes an average 5 minutes for preparation of bill and delivery of
the item .Calculate the following
i. Counter utilisation level [1 Mark]
ii. Average waiting time of the customers at the fast food joint [1 Mark]
iii. Expected average waiting time in the line [1 Mark]
iv. Average number customers in the service counter area [1 Mark]
v. Average number of customers in the line [1 Mark]
vi. Probability that the counter clerk is idle [1 Mark]
vii. Probability of finding the clerk busy [1 Mark]
viii. Chances that the clerk is required to wait for more than 30 minutes in the system [1 Mark]
ix. Probability of having four customers in the system [1 Mark]
x. Probability of finding more than 3 customers in the system. [1 Mark]
[Total: 20 Marks]
Question Five
a) Outline Monte Carlo simulation steps [5 Marks]
b) Based on the weather conditions and industrial development in new AWENDO industrial belt, the
demand for petrol for vehicles on a new service station follows the under mentioned distribution.
Weekly Demand Probability
2,000 litres 0.12
3,000 litres 0.23
4,000 litres 0.48
5,000 litres 0.17
The petrol is received from the depot only once a week and the storage capacity is only 5,500 litres.
Initial supply is 3,500 litres.
Required
Work out a 10 week petrol order pattern using the following random numbers 23, 78, 95, 05, 29,
76,27,57,32 and 81. [15 Marks]
[Total: 20 Marks]
More Question Papers
Popular Exams
Return to Question Papers