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PG-598
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II Semester M.B.A. Degree Examination, July 2018 (CBCS Scheme)
MANAGEMENT
2.6: Quantitative Techniques and Operation Research
Time: 3 Hours Max. Marks :70
Instruction: Calculators and tables are allowed.
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SECTION - A
Answer any five of the following questions, each question carries five marks. (5x5=25)
- Discuss the assumptions of Replacement Theory.
- Explain the role and importance of operation research in managerial decisions.
- Explain with examples how linear programming is useful for decision making.
- Solve graphically
Maximize Z = 5x1 + 4x2
Subject to 4x1 + x2 = 40
2x1 + 3x2 = 90
where x1, x2 = 0 - A telephone repairman finds that the time spent on his job has an exponential distribution with a mean of 20 minutes. If he repairs sets in the order in which they came in and if the arrival of sets fallows a poisson distribution approximately with an average rate of 10 per hour day. What is the repairman's expected idle time each day? How many Jobs are ahead of the average set just brought in ?
- Solve the assignment problem for minimum optimal cost
1 2 3 4 5 A 8 4 2 6 1 B 0 9 5 5 4 C 3 8 9 2 6 D 4 3 1 0 3 E 9 5 8 9 5
Persons - There are Four Jobs to be processed on each of the five Machines A, B, C, D and E in the order ACDBE. Find the total minimum elapsed time, if no passing jobs is permitted.
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A B C D E J1 7 5 2 3 9 J2 6 6 4 5 10 J3 5 4 5 6 8 J4 8 3 3 2 6
Machines
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SECTION - B
Answer any three of the following, each question carries ten marks. (3x10=30)
- What is game theory ? Explain the assumptions made in the game theory. How it is helpful for business?
- Solve the following LPP by Simplex Method.
Max Z = 20x1 + 6x2 + 8x3
Subject to 8x1 + 2x2 + 3x3 = 200
4x1 + 3x2 = 100
2x2 + x3 = 50--- Content provided by FirstRanker.com ---
where x1, x2 and x = 0 - A project consists of the following activities, whose time estimates are given against each as under:
Activity Optimistic Most likely Pessimistic 1-2 3 6 15 1-3 2 5 14 1-4 6 12 30 2-5 2 5 8 2-6 5 11 17 3-6 3 6 15 4-7 3 9 27 5-7 1 4 7 6-7 4 19 28
Required:
1) Draw the project network.--- Content provided by FirstRanker.com ---
2) Determine the critical path and the expected project duration.
3) What is the probability that the project will be completed in 40 weeks ?
4) What project duration will have 95% chance of completion ? - A computer has 2000 electronic tubes maximum life of which is 500 hours. The probability of failure at different periods of time is as follows :
Period (100 hours) Age at failure (Hrs) Probability of failure 1 0-100 0.10 2 101-200 0.26 3 201-300 0.35 4 301-400 0.22 5 401-500 0.07 --- Content provided by FirstRanker.com ---
Replacement of an individual tubelight failing during service costs 60 per tube, while in case of group replacement at fixed interval is 15 per tube.
i) How the replacement should be done
a) Individually or b) in group
ii) When the tubes should be replaced. - Case study (compulsory):
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SECTION - C (15x1=15)
A company has 3 factories and 4 customers. The company furnishes the following schedule of profit per unit on transportation of its goods to the customers in rupees.
| Customers | A | B | C | D | Supply |
|---|---|---|---|---|---|
| P | 40 | 25 | 22 | 33 | 100 |
| Q | 44 | 35 | 30 | 30 | 30 |
| R | 38 | 38 | 28 | 30 | 70 |
| Demand | 40 | 20 | 60 | 30 |
You are required to solve the transportation problem to maximize the profit and determine the resultant optimal profit.
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