Operations Research- Paper 2
Section I
Q1. Explain the following concepts: (3 X 5= 15)
- Principle behind balanced assignment problem
- Decision taking under uncertainty
- Unbound solution in graphical
- CPM vs PERT
- Alternate solution in LPP
Q2. A company manufactures and sells 3 varieties of pressure cookers. Supply of aluminum is limited to 750 kgs per week and the machine is available for 600 hours per week. The resource usage and profitability of each model is given as follows:        (15)
| Model 1 | Model 2 | Model 3 | |
| Aluminum | 6 | 3 | 5 |
| Machine | 3 | 4 | 5 |
| Contribution | 60 | 20 | 80 |
- Formulate a LPP and solve by simplex (10 marks)
- What would happen if additional 150 kgs of aluminium is made available(2 mark)
- A new model has been developed that would require 3 kg of aluminium and 3 hrs on the machine and would give a profit of Rs 40. Should it be introduce.(3 marks)
Section II (solve any 3)
Q3 – The data pertaining to a project is given below                                  (10)
|
Activity |
Preceeding activity |
Optimistic time |
Most likely time |
Pessimistic time |
|
A |
– |
4 |
6 |
8 |
|
B |
A |
5 |
7 |
15 |
|
C |
A |
4 |
8 |
12 |
|
D |
B |
15 |
20 |
25 |
|
E |
B |
10 |
18 |
26 |
|
F |
C |
8 |
9 |
16 |
|
G |
E |
4 |
8 |
12 |
|
H |
D,F |
1 |
2 |
3 |
|
I |
G,H |
6 |
7 |
8 |
- Compute the critical path and time
- What is the probability that the assignment would be complete in 55 days
- What number of days has the probability of covering the task in 90 percent
(area under 2.29= 0.4890 and area under 1.28= 0.40)
Q 4. 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 which are suitable for the installation. Because of extra large size, M2 cannot be placed at C and M3 cannot be placed at A. The cost of installing machines location wise in hundred rupees is as follows:
| A | B | C | D | E | |
| M1 | 9 | 11 | 15 | 10 | 11 |
| M2 | 12 | 9 | X | 10 | 9 |
| M3 | X | 11 | 14 | 11 | 7 |
| M4 | 14 | 8 | 12 | 7 | 8 |
Find the optimal assignment.
Q 5. The following transportation sum is solved and given
| Â | D1 | D2 | D3 | D4 | SUPPLY |
| O1 | 5 | 10 | 4 (100) | 5 | 100 |
| O2 | 6 (200) | 8 | 7 | 2 (50) | 250 |
| O3 | 4 (50) | 2 (100) | 5 (50) | 7 | 200 |
| DEMAND |
250 | 100 | 150 | 50 |
Is the above solution optimum. What would the new solution be if cost from O2-D3 changes from 7 to 6.
Q 6. A. The research department of Hindustan Unilever has recommended to the marketing department to launch a shampoo of three different types. The marketing manager has to decide about the type of shampoo to be launched under the following estimated pay-offs for various levels of sales:
| Types of shampoo | Estimated levels of sales | ||
| 15000 | 10000 | 5000 | |
| Egg shampoo | 30 | 10 | 10 |
| Clinic Shampoo | 40 | 15 | 5 |
| Delux shampoo | 55 | 20 | 3 |
What will be the marketing manager’s decision if:
i)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Maximin ii)Â Maximax iii)Â Laplace and iv) Minimax (Regret)Â criterion is applied(4 marks)
B. Returns of 2 stocks A1 and A2 are given. Draw a decision tree to choose one of them
| Stocks | Economic Conditions | |||
| Recession | Stable economy | Moderate growth |
Boom |
|
| A1 | 50 | 90 | 120 |
170 |
| A2 | -10 | 50 | 270 |
420 |
| Probability | 0.10 | 0.25 | 0.30 |
0.35 |
Prof Vipin Saboo can be contacted on 9820779873 for any further clarifications.
2 Comments