Download JNTUH MCA 2nd Sem R13 2018 January 812AK Operations Research Question Paper

Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 2nd Sem (Second Semester) Regulation-R132018 January 812AK Operations Research Previous Question Paper


R13

Code No: 812AK















JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

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.



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 ? 4 Marks = 20




1.a) Explain briefly the major phases of operations research.







[4]

b) Distinguish between the transportation model and the assignment model.

[4]

c)

Explain the various types of replacement situations.







[4]

d)

Explain the bellman's principle of optimality.









[4]

e) What is queue? Explain basic elements of queues.







[4]





PART - B

















5 ? 8 Marks = 40

2.

Solve the following LPP using the simplex method.



Max Z=x1-x2+3x3

Subject to x1+x2+x310

2x1-x33



2x1-2x2+3x30

and x1, x2, x30

















[8]

OR

3.

Use simplex method to



Minimize Z= 2x1+9x2+x3 subject to constraints:



x1+4x2+2x35



3x1+x2+2x34

















[8]



x1>0, x2>0, x3>0


4.

Solve the following travelling salesman problem and find the shortest possible path.

























[8]





A

B

C

D

E





A



3

6

2

3



B

3



5

2

3




C

6

5



6

4



D

2

2

6



6




E

3

2

4

6






OR






5.

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



O2

2

4

0

1

38




O3

1

2

-2

5

32



Demand 40

28

30

32





6.

The cost of the machine is Rs 6100/- and its scrap value is Rs 100/-. The maintenance



cost found from experience are as follows:













Year

1

2

3

4

5

6

7

8




Maintenance 100 250 400 600 900 1200 1600 2000



cost(Rs)



When should the machine be replaced?











[8]



OR

7.

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

9

6

3

1


8.

Solve the following problem using forward dynamic programming.



Min Z=x 2

2

2

1 +x2 +x3



Subject to x1+x2+x315



And x1, x2, x30

















[8]

OR

9.

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]




Player B









3

2

4

0



Player A 2

4

4

2







4

2

4

0



0

4

0

8








10.

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

11.

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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This post was last modified on 17 March 2023