JNTU
JNTU B.Tech IV OPERATIONS RESEARCH Previous Question Paper (May/June - 2019 - R15)
Note: This question paper contains two parts A and B. Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks and may have a, b, c as sub questions.
Part A
Write the phases of operations research.
Answer
The phases of operations research are: 1) Defining the problem, 2) Constructing a mathematical model, 3) Solving the model, 4) Validating the model, and 5) Implementing the solution.
What are the artificial variables? State their role in solving the LPP model.
Answer
Artificial variables are non-negative variables introduced in LPP constraints (typically with '≥' or '=' signs) to provide an initial basic feasible solution when a slack variable cannot serve as a starting basis. Their role is to facilitate the start of the Simplex method (via Big-M or Two-Phase methods) by acting as a temporary basis, and they must be driven to zero for the final solution to be feasible for the original problem.
Explain North-West corner method for finding initial BFS.
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State the travelling salesman problem.
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State the conditions under which 3 machine n jobs sequencing problem is equivalent 2 machine and n jobs sequencing problem.
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Derive the optimal replacement policy when time value of money is considered.
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Write the expressions for determining Mixed strategy for 2×2 games without saddle point.
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Define i) set up cost ii) holding cost.
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Write expression for average number of customers present in the basic queuing model and define associated terms.
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State the Bellman’s principle of optimality.
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Part B
Define model. Classify models according to the purpose for which they are developed.
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A company produces two types of hats. Each hat of first type requires twice as much as labour time as second type. If all hats are of the second type only, the company can produce a total of 500 hats a day. The market limits daily sales of the first and second type to 150 and 250 hats. Assuming that the profits per hat are Rs.8 for type A and Rs.5 for type B, formulate the problem as linear model in order to determine the number of hats to be produced of each type so as to maximize the profit and solve it by graphical method.
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Solve the following LPP problem by two-phase method: Max = 2x1 + 3x2 + 5x3 Subject to 3x1 +10x2 + 5x3 <= 15; 33x1-10x2 +9x3 <= 33; x1+2x2+3x3 >= 4; x1, x2, x3 >= 0
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A company has three factories I,II,III and four warehouses 1, 2, 3, 4. The transportation cost (in Rs.) per unit from each factory to each warehouse is given in the table. The requirements of each warehouse and the capacity of each factory are given below. Find the minimum cost of transportation schedule with initial BFS is through Vogels method.
| 1 | 2 | 3 | 4 | Availability | |
|---|---|---|---|---|---|
| I | 25 | 17 | 25 | 14 | 400 |
| II | 15 | 10 | 18 | 24 | 600 |
| III | 16 | 20 | 8 | 13 | 600 |
| Req | 300 | 300 | 500 | 500 |
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A company has a team of four salesmen and there are four districts. Profit per day in rupees for each salesman in each district is as below. Find the assignment of salesmen to various districts which will yield maximum profit.
| 16 | 10 | 14 | 11 |
| 14 | 11 | 15 | 15 |
| 15 | 15 | 13 | 12 |
| 13 | 12 | 14 | 15 |
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Two jobs are to be processed on four machines A, B, C and D. The technological order for these jobs on machines is as follows: Job 1: A-B-C-D; Job 2: D-B-A-C. Processing times: Job 1(A:4, B:6, C:7, D:3), Job 2(A:4, B:7, C:5, D:8). Solve it by graphical method.
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The failure rates observed for light bulbs are (End of week: 1-8; Probability: 0.05, 0.13, 0.25, 0.43, 0.68, 0.88, 0.96, 1.00). Cost of individual replacement is Rs.1.25. Cost of group replacement is 30 paise per bulb. What is the best interval between group replacement? At what group replacement price per bulb would a policy of strictly individual replacement become preferable to the adopted policy.
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Solve the following game by using the principle of dominance:
4 2 0 2 1 1
4 3 1 3 2 2
4 3 7 -5 1 2
4 3 4 -1 2 2
4 3 3 -2 2 2Answer
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Annual demand = 5400 units. Ordering cost = Rs.600. Carrying cost = 30%. Price breaks: (0-2400: Rs.12), (2400-3000: Rs.10), (3000+: Rs.08). Find the optimal order size. If the order cost is changed to Rs.200 per order, find the optimal order size.
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Explain the Kendal notations for representing the queuing model.
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A television repairman finds that the time spent on his jobs has an exponential distribution with a mean of 30 minutes. If he repairs the sets in the order in which they came in and if the arrival of sets follows a Poisson distribution with an approximate average rate of 10 per 8-hour day, what is the repairman‘s expected idle time each day? How many jobs are ahead of the average set just brought in?
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Minimize y1^2 + y2^2 + y3^2 subject to y1 + y2 + y3 = 15 using Bellman’s principle.
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