Madras University (UnOM) 2008 M.B.A Business Administration Applied OR - Question Paper
MAY 2008 P/ID 37508/PBAH
(6 pages)
Maximum: 80 marks PART A (5 x 5 = 25 marks)Time: Three hours
1. Briefly discuss the steps involved in solving Operations Research problem.
2. What do you mean by degeneracy in simplex method? How it could be overcome?
3. Solve Graphically
Maximize Z 2xt + 3xa
&t *, + x2 & 30 x2 >3 x, S12 x, -x2 0 x, 5 20
where x,,x2 SO.
4. How feasible solution could be obtained Tor transportation problem? Explain any two methods.
5. Draw a project network for the following activities and find critical path.
Activity Duration (days)
|
1-2 |
4 |
|
1-3 |
12 |
|
1-4 |
10 |
|
2-4 |
8 |
|
2-5 |
6 |
|
3-6 K |
8 |
|
4-6 D |
Kx 10 |
|
6-7 \ |
Y1 * io |
|
6-7 |
\ 0 |
|
6-8 |
8 |
|
7-8 |
10 |
|
8-9 |
6 |
6. Explain the operating characteristics of queuing system.
7. Explain how pure strategy can be analyzed.
8. Discuss the advantages and limitations of LP model.
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PART B (4 x 10 = 40 marks)
Answer any FOUR questions.
All questions carry equal marks.
9. Solve the following LPP.
Minimile Z = 4xi + x2
B.t 3xt +ara 3 4x, +3x2 X| +2*2 3
where *i,x2 2 0.
10. The following table shows all the necessary information on the available supply to each warehouse, the requirement of each market and the unit transportation cost in rupees from each warehouse to each market.
Market
Warehouse
Requirement
I II III IV Supply
|
A |
5 |
2* |
3* |
22 |
|
B |
4 |
8 |
lv6 |
15 |
|
C |
4 |
6 |
7\ 5 |
8 |
|
7 |
12 |
17 9 |
\
The shipping clerk has worked out the following schedule from experience :
12 units from A to II, 1 unit from A to HI, 9 units from. A to IV, 15 units from B to ill, 7 units from C to I and 1 unit from C to III
(a) Check and See if the clerk has made the optimal schedule.
(b) Find the optimal schedulo and minimum total shipping cost.
11. A project is composed of seven activities whose time estimates are listed in the table
Activity Estimated Duration (Weeks)
|
1-2 |
Optimistic 1 |
Most likely 1 |
Pessimistic 1 |
|
1-3 |
1 |
4 |
7 |
|
1-4 |
2 |
2 |
8 |
|
2-5 |
1 |
1 |
1 |
|
3-5 |
2 |
5 |
14 |
|
4-6 |
2 |
5 |
8 |
|
6-6 |
3 |
6 |
16 |
(a) Draw the project network.
<b) Find the expected duration and variance of each activity.
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fP.T.O.J
(c) Calculate early and late occurrence time for each event. What is the expected project length.
(d) if the project due date is 19 weeks, what is the probability of meeting the due date?
12. Reduce the following game by dominances and find the value of the game.
Player B
|
I |
II |
III |
IV | |
|
I |
3 |
2 |
4 |
0 |
|
11 |
3 |
4 |
2 |
4 |
|
III |
4 |
2 |
4 |
0 |
|
IV |
0 |
4 |
0 |
8 |
13. A manufacturer has to supply his customer with 600 units of his product per year. Shortages arc not allowed and storage cost amounts to 60 paise per unit per year. The set up cost is Rs. 80. Find
(a) EOQ
(b) Minimum average yearly cost
(c) The optimum number of order per day
(d) The optimum period of supply per optimum
order
(e) The increase in the total cost associated with ordering 20% higher than EOQ.
14. Customers arrive at a first class ticket counter of a theater at a rate of 12 per hour. There is one clerk serving the customers at the rate of 30 per hour
(a) What is the probability that there is no customer in the counter?
(b) What is the probability that there are more than 2 customers in the counter?
(c) What is the probability that there is no customer waiting to be served?
(d) What is the probability that a customer is being served and nobody in waiting?
PART C {1 x 15 * 15 marks) (Compulsory)
15. The following mortality rates have been observed for a certain type of light bulbs
Week: 1 2 3 4 5
Percent failing by the
end of week 10 25 50 80 100
There are 1000 bulbs in use and its costs Re. 1 to replace an individual bulb which has burnt out. If all bulbs were replaced simultaneously it would cost 25 paisc per bulbs. It is proposed to replace all bulbs aL fixed intervals whether or not they have burnt out and to continue replacing burnt out bulbs as they fall. At what intervals should all the bulbs be replaced?
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Attachment: |
| Earning: Approval pending. |
