Code No: 812AK
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
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MCA II Semester Examinations, January - 2018
OPERATIONS RESEARCH
Time: 3hrs Max.Marks:60
Note: This question paper contains two parts A and B.
Part A is compulsory which carries 20 marks. Answer all questions in Part A.
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Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 8 marks and may have a, b, c as sub questions.
PART - A 5 x 4 Marks = 20
- a) Explain briefly the major phases of operations research.
- b) Distinguish between the transportation model and the assignment model.
- c) Explain the various types of replacement situations.
- d) Explain the bellman’s principle of optimality.
- e) What is queue? Explain basic elements of queues.
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PART -B 5 x 8 Marks = 40
- Solve the following LPP using the simplex method.
Max Z=x1-X,+3X3--- Content provided by FirstRanker.com ---
Subject to x;+x+x3<10
2X1-X3§3
2X1 -2X2+3 X3§0
and x, Xp, Xx3>0 [8]
OR - Use simplex method to
Minimize Z= 2x1+9x2+4x3 'subject to constraints:
X1+4X2+2X325
3x1+x01+2x3>4 [8]
x>0, x>0, x3>0 - Solve the following travelling salesman problem and find the shortest possible path. [8]
ORA B C D E A 0 3 6 2 3 B 3 0 5 2 3 C 6 5 0 6 4 D 2 2 6 0 6 E 3 2 4 6 0 - Find the basic feasible solution with cost using Vogel’s approximation method. Find the optimal solution. [8]
D1 D2 D3 D4 supply o1 1 2 -2 3 70 02 2 4 0 1 38 o3 1 2 -2 5 32 Demand 40 28 30 32 - The cost of the machine is Rs 6100/- and its scrap value is Rs 100/-. The maintenance cost found from experience are as follows:
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When should the machine be replaced? [8]Year 1 2 3 4 5 6 7 8 Maintenance cost(Rs) 100 250 400 600 900 1200 1600 2000
OR - A machine operator has to perform two operations turning and threading on a number of different jobs. The time required to perform these operations for each job is known. Determine the order in which the jobs should be processed in order to minimize the total time required to complete all the jobs. [8]
Machine/Job 1 2 3 4 5 6 A 3 12 5 2 9 11 B 8 10 2 19 6 3 - Solve the following problem using forward dynamic programming.
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Min Z=x1²+x2²+x3²
Subject to x1+x+x3>15
And x1, X, X320 [8]
OR - Obtain the optimal strategies for both persons and the value of the game for zero-sum two-person game whose payoff matrix is given below: [8]
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Player B Player A 3 2 4 0 5 7 2 5 4 2 4 0 0 4 0 8 - A particular item has demand of 5000 units/year. The cost of procurement is Rs200 and the holding cost per unit is Rs 2.40/year. The replacement is instantaneous and no shortages are allowed. Determine: a) The economic lot size, b) The time between orders, c) The number of orders per year. d) The total cost per year if the cost of one unit is Rs 2. [8]
OR - Jobs arrival at a workstation in a manufacturing plant is in a Poisson fashion at an average rate of five per hour. The time to machine one job is an exponential distribution with a mean time of 20 minutes. What is the expected time a job has to wait at the workstation? What will be the average number of jobs waiting at the workstation at any time? What is the probability that there will be more than four jobs? [8]
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