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Dms 201 Operations Research I Question Paper
Dms 201 Operations Research I
Course:Diploma In Business Management
Institution: Kca University question papers
Exam Year:2014
UNIVERSITY EXAMINATIONS: 2013/2014
STAGE V ORDINARY EXAMINATION FOR THE DIPLOMA IN
BUSINESS MANAGEMENT
DMS 201 OPERATIONS RESEARCH I
DATE: AUGUST 2014
TIME: 1 1/2 Hours
INSTRUCTION: Answer any THREE questions
QUESTION ONE: (20 MARKS)
a) Enumerate four basic assumptions of a transportation problem
(4 Marks)
b) A cement company has three factories which manufacture cement at which it is then
transported to four distribution centers. The quality of monthly production of each
factory, the demand of each distribution center and the associated transportation cost per
unit in Kshs. are given as follows:
Factories
Distribution centers
W
X
Monthly
Y
Z
production
(units)
A 10 8 5 4 7000
B 7 9 15 8 8000
C 6 10 14 8 10000
Monthly demand 6000 6000 6000 5000
(units)
Required:
(i) Suggest the optimal transportation schedule (14 Marks)
(ii) Obtain the total transportation cost in such a case. (2 Marks)
1
QUESTION TWO: (20 MARKS)
a) Distinguish between transportation and assignment problems
(4 Marks)
b) Smith Corporation has four salesmen each of them can be assigned any of the four sales
territories. Estimates of the sales revenues in hundreds of shillings for each salesman are
as given below:
Salesman
Sales territories
1 2 3 4
A 65 78 83 60
B 85 52 59 44
C 83 56 69 64
D 49 80 85 84
Required
(i) Obtain the optimal assignment that maximizes the sales revenue. (10 Marks)
(ii) Build a linear programming problem for the above problem. (6 Marks)
QUESTION THREE: (20 MARKS)
The following list of activities must be accomplished in order to complete a construction project:
Activity
Predecessors
Time (in weeks)
A None 3
B None 8
C A,B 4
D B 2
E A 1
F C 7
G E,F 5
H D,F 6
I G,H 8
J I 9
2
Required:
(i) Construct a network for the construction project (10 Marks)
(ii) Find the critical path and duration for the project (2 Marks)
(iii) Compute the total float for each activity (8 Marks)
QUESTION FOUR: (20 MARKS)
a)
Using a diagram, explain the rationale underlying the economic order quantity
model.(The mathematical derivation is not required)
(4 Marks)
b) Explain briefly the assumptions of economic order quantity.
(4 Marks)
c) Olivya company ltd is located in Industrial area in Nairobi. The company manufactures a
product branded “Que” which is used in the building industry. The main raw material
used in the manufacture of “Que” is material B4 2014.
The following information relates to material B4 2014.
Annual requirements 300,000 units
Ordering costs Shs.6,000 per order
Annual holding costs 20% of the purchase price
Purchase price per unit Shs.80
Required
(i) The economic order quantity. (4 Marks)
(ii) The number of orders needed per year. (2 Marks)
(iii) Total cost of ordering and holding material B4 2014per year. (6 Marks)
QUESTION FIVE: (20 MARKS)
a) Outline any five assumptions of the linear programming model
b) A company produces two products A and B. The standard revenues and cost per unit of
the product are:
3
(5 Marks)
Product
A
B
Sh
sh
Selling price
sh
200
sh
180
Variable cost:
Material z (sh 10 per kg)
40 40
Direct labour (sh 8 per hour) 32 40
Packaging (sh 12 per hour) 12 24
Other variable cost 76 70
Additional information:
1. The maximum available inputs per week are limited as follows:
Material Z 120 kilogrammes
Direct labour 100 hours
Packaging time 50 hours
Required:
(i) formulate a linear programming model to solve the above problem (6 Marks)
(ii) Graphically solve the linear programming model formulated above. (9 Marks)
4
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