Prelim- Operations Research-
Q1. Solve any 2 (15 marks)
- 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. Formulate and solve by simplex
| Model 1 | Model 2 | Model 3 | |
| Aluminum | 6 | 3 | 5 |
| Machine | 3 | 4 | 5 |
| Contribution | 60 | 20 | 80 |
- A company manufactures two products A and B. Profit per unit of A and B are Rs 3, 5 respectively. Each unit of A and B requires 3 and 2 units of labour hours. The company has a maximum of 18 labour hours available. Also the maximum demand for A and B is limited to 4 and 6 units respectively. Formulate the above as LPP and solve by Graphical.
- Explain the concepts:- Redundancy in graphical, Shadow prices, Degeneracy in simplex
Q2. The following information is available for a network. Indirect cost id Rs 300 per day. Time give is in days (15 marks)
| Job | 1—2 | 1–3 | 2—3 | 2–4 | 2–5 | 3–6 | 4–5 | 5–6 |
| Normal time | 9 | 15 | 7 | 7 | 12 | 12 | 6 | 9 |
| Normal cost | 1300 | 1000 | 1000 | 1200 | 1700 | 600 | 1000 | 900 |
| Crash time | 4 | 13 | 4 | 3 | 6 | 11 | 2 | 6 |
| Crash cost | 2400 | 1380 | 1540 | 1920 | 2240 | 700 | 1600 | 1200 |
Draw the network diagram and find the critical path and corresponding cost. What would be the impact on the cost if the deadline of 27days is imposed?
Q3. Solve any 2(15 marks)
- Â Consider the problem of assigning 4 clerks to 4 tasks. Time in hours taken by each is given below.
| Â | Tasks | |||
| Clerks | A | B | C | D |
| I | 4 | 7 | 5 | 6 |
| II | 3 | 8 | 7 | 4 |
| III | 3 | 5 | 5 | 3 |
| IV | 6 | 6 | 4 | 2 |
Clerk II cannot be assigned A and Clerk III cannot be assigned B. Find the optimum allocation.                                                                                                                      How do you find out that an alternate solution exists in the assignment sum.
- 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.
- Â Â Â Explain the concepts of Regret matrix in assignment, Degeneracy in Transportation, MODI
Q4. Solve any 2( 15 marks)
- For the following data compute EMV, EPPI, EVPI and EOL
| Probability | S1 | S2 | S3 | S4 | S5 |
| 0.1 | 20 | 12 | 4 | -4 | -12 |
| 0.2 | 20 | 22 | 14 | 6 | -2 |
| 0.4 | 20 | 22 | 24 | 16 | 8 |
| 0.2 | 20 | 22 | 24 | 26 | 18 |
| 0.1 | 20 | 22 | 24 | 26 | 28 |
- A company is planning to buy a machine at Rs 50,000. It is anticipated that if the machine is purchased the demand can go up and hence the revenues gained would be Rs 75,000. If the demand is not good there is a loss of Rs 20,000. The company feels that there are 70% chances that demand being good and 30% chances of a bad demand. Construct a decision tree and help the company decide whether the machine should be purchased or no.
- 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:
Maximin ii)Â Maximax iii)Â Laplace and iv) Minimax (Regret)Â criterion is applied
Q 5. Solve any 2(15 marks)
- The data pertaining to a project is given below
| 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)
- For the following activity compute ES, EF, LS, LF and TF
| Activity | Predecessor | Duration |
| A | None | 3 |
| B | None | 8 |
| C | B | 6 |
| D | B | 5 |
| E | A | 13 |
| F | A | 4 |
| G | F | 2 |
| H | C,E,G | 6 |
| I | F | 2 |
Explain the following :- 3 time estimate in PERT, CPM vs PERT, Updating in networking.
For any doubts, contact :
Prof Vipin Saboo 9820779873                                                 Â
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