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Operations Research Question Paper
Operations Research
Course:Bachelor Of Commerce
Institution: University Of Nairobi question papers
Exam Year:2012
UNIVERSITY OF NAIROBI
MODULE II DEGREE PROGRAMME 2012/2013 (NAIROBI EVENING)
FOURTH YEAR EXAMINATIONS FOR THE DEGREE OF BACHELOR OF COMMERCE
DOM 311: OPERATIONS RESEARCH
DATE: DECEMBER 20, 2012 TIME: 6:00 P.M. – 8:00 P.M.
INSTRUCTIONS
1. The paper contains FOUR Questions
2. Attempt ALL
3. Show your work clearly
QUESTION ONE
Amalgamated Engineering makes two kinds of gearbox, manual and automatic. There are four stages of these gearboxes, with details of time needed and weekly availabilities given below. The company makes a profit of Sh. 64 on each manual gearbox sold and Sh. 100 on each automatic gearbox sold.
State in
Manufacture Time Needed (Hour per Unit) Time Available
(Hours per Week)
Manual Automatic
Foundry 3 5 7,500
Machine Shop 5 4 10,000
Assembly 2 1 3,500
Testing 1 1 2,000
REQUIRED
a) Formulate this problem as a linear programming model (10 marks)
b) Using Simplex Method, find the optimal solution (15 marks)
QUESTION TWO
In the modification of a plant layout of a factory, four new machines M1, M2, M3 and M4 are to be installed in a machine shop. There are five vacant places A, B, C, D and E available. Because of limited space, machine M2 cannot be placed at C and M3 cannot be placed at A. the cost of locating machine i and j in shillings is shown below:
MACHINE PLACE
A B C D E
M1 9 11 15 10 11
M2 12 9 - 10 9
M3 - 11 14 11 7
M4 14 8 12 7 8
REQUIRED
Determine the optimal assignment schedule. (25 marks)
QUESTION THREE
(a) The New Embakasi District Hospital buys a certain antibiotic from Dawa Suppliers. The drug can be bought at the following prices:
ORDER SIZE PRICE PER UNIT
1-4,999 Sh. 2.75
5,000-9,999 Sh. 2.60
10,000 and more Sh. 2.50
The demand for the drug in the hospital is 50,000 units a year. There is an ordering cost of Sh. 50 per order and a holding cost of 20% of the cost of the item per unit per year.
REQUIRED
Determine the optimal purchasing policy for the hospital. (21 marks)
(b) Energy Solution Company produces a certain energy-saving device. Demand for the device is 1,800 units per year. The company can produce at an annual rate of 7,200 units. Set-up cost is Sh. 300. There is an inventory holding cost of Sh. 36 per unit, per year.
REQUIRED
Determine the optimal economic lot size. (4 marks)
QUESTION FOUR
An Aerospace Company at Wilson Airport received a contract for the final assembly of a space module for the upcoming space mission experiment. A team of engineers has determined activities, precedence relationships and time estimates in weeks as given below:
ACTIVITY
DESCRIPTION
PREDECESSOR DURATION (WEEKS)
a m b
A Construct a shell of module
- 25 30 45
B Order life-support system and scientific experimentation package
- 10 15 20
C Order components of control and navigation system
- 20 25 35
D Wire module A 3 3 5
E Assemble control and navigational system C 5 7 12
F Preliminary test of life-support system B 1 1 1
G Install life-support system in module D,F 4 5 7
H Install scientific experimentation package module D,F 2 2 3
I Preliminary test of control and navigation system D,E,F 4 4 6
J Install control H,I 8 10 14
K Final testing G,J 6 8 15
REQUIRED
a) Draw the network diagram (10 marks)
b) Determine the critical activities, critical path and project duration (3 marks)
c) Calculate the floats on the non-critical activities and interpret their meaning (7 marks)
d) What is the probability of completing the project within 64 weeks? (5 marks)
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