Download JNTUA (JNTU Anantapur) MCA (Master of Computer Applications) 2014 August Supplementary 2nd Sem 9F00205 Operations Research Question Paper

Code: 9F00205

MCA II Semester Regular & Supplementary Examinations August 2014

OPERATIONS RESEARCH

(For students admitted in 2009, 2010, 2011, 2012 & 2013 only)

Time: 3 hours Max. Marks: 60

Answer any FIVE questions

All questions carry equal marks

1. (a)

Discuss the importance of operations research in decision making process.

(b)

? ???? 1

+ 2 ???? 2

? 8, ???? 1

+ 2 ???? 2

? 12

Use simple method to solve the following LPP

Maximize z = ???? 1

+ 2 ???? 2

subject to

???? 1

? 2 ???? 2

? 3; ???? 1

? 0 ???????????? ???? ? 0.

(c) Use two phase simplex method to minimize Z = ???? 1

+ ???? 2

+ ???? 3

subject to the

constraints ???? 1

? 3 ???? 2

+ 4 ???? 3

= 5,

???? 1

? 2 ???? 2

? 3, 2 ???? 2

? ???? 3

? 4; ???? 1

? 0 ???????????? ???? ? 0 and

???? 3

is unrestricted.

2. (a) Use duality to solve the following LPP

Maximize Z = 2 ???? 1

+ ???? 2

subject to the constraints

???? 1

+ 2 ???? 2

? 10, ???? 1

+ ???? 3

? 6,

???? 1

? ???? 2

? 2, ???? 1

? 2 ???? 2

? 1; ???? 1

, ???? 2

? 0.

(b) Use dual simplex method to solve the LPP

Maximize Z = ?3 ???? 1

? ???? 2

subject to the constraints

???? 1

+ ???? 2

? 1, 2 ???? 1

+ 3 ???? 2

? 2; ???? 1

, ???? 2

? 0.

3. (a) Use Vogel?s approximation method to obtain an initial basic feasible solution of the

transportation problem

D E F G Available

A

B

C

?

11 13 17

16 18 14

21 24 13

14

10

10

?

250

300

400

(b)

What is an assignment problem and how do you interpret it as an L.P model?

4. (a)

Find the sequence that minimizes the total elapsed time (in hours) required to complete

the following tasks on two machines.

Task A B C D E F G H I

Machine I 2 5 4 9 6 8 7 5 4

Machine II 6 8 7 4 3 9 3 8 11

(b) Use graphic method to find the minimum elapsed total time sequence of 2 jobs and 5

machines, when we are given the following information machines.

A B C D E

2 3 4 6 2

Job I ?

Sequence:

Time in hours:

C A D E B

4 5 3 2 6

Job I ?

Sequence:

Time in hours:

Continued in page 2

Page 1 of 2

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Code: 9F00205

MCA II Semester Regular & Supplementary Examinations August 2014

OPERATIONS RESEARCH

(For students admitted in 2009, 2010, 2011, 2012 & 2013 only)

Time: 3 hours Max. Marks: 60

Answer any FIVE questions

All questions carry equal marks

1. (a)

Discuss the importance of operations research in decision making process.

(b)

? ???? 1

+ 2 ???? 2

? 8, ???? 1

+ 2 ???? 2

? 12

Use simple method to solve the following LPP

Maximize z = ???? 1

+ 2 ???? 2

subject to

???? 1

? 2 ???? 2

? 3; ???? 1

? 0 ???????????? ???? ? 0.

(c) Use two phase simplex method to minimize Z = ???? 1

+ ???? 2

+ ???? 3

subject to the

constraints ???? 1

? 3 ???? 2

+ 4 ???? 3

= 5,

???? 1

? 2 ???? 2

? 3, 2 ???? 2

? ???? 3

? 4; ???? 1

? 0 ???????????? ???? ? 0 and

???? 3

is unrestricted.

2. (a) Use duality to solve the following LPP

Maximize Z = 2 ???? 1

+ ???? 2

subject to the constraints

???? 1

+ 2 ???? 2

? 10, ???? 1

+ ???? 3

? 6,

???? 1

? ???? 2

? 2, ???? 1

? 2 ???? 2

? 1; ???? 1

, ???? 2

? 0.

(b) Use dual simplex method to solve the LPP

Maximize Z = ?3 ???? 1

? ???? 2

subject to the constraints

???? 1

+ ???? 2

? 1, 2 ???? 1

+ 3 ???? 2

? 2; ???? 1

, ???? 2

? 0.

3. (a) Use Vogel?s approximation method to obtain an initial basic feasible solution of the

transportation problem

D E F G Available

A

B

C

?

11 13 17

16 18 14

21 24 13

14

10

10

?

250

300

400

(b)

What is an assignment problem and how do you interpret it as an L.P model?

4. (a)

Find the sequence that minimizes the total elapsed time (in hours) required to complete

the following tasks on two machines.

Task A B C D E F G H I

Machine I 2 5 4 9 6 8 7 5 4

Machine II 6 8 7 4 3 9 3 8 11

(b) Use graphic method to find the minimum elapsed total time sequence of 2 jobs and 5

machines, when we are given the following information machines.

A B C D E

2 3 4 6 2

Job I ?

Sequence:

Time in hours:

C A D E B

4 5 3 2 6

Job I ?

Sequence:

Time in hours:

Continued in page 2

Page 1 of 2

Code: 9F00205

5. (a) A firm is considering replacement of a machine, whose cost price is Rs12,200 and the

scrap value Rs 200. The running (maintenance and operating) costs in Rs are found

from experience to be as follows.

Year: 1 2 3 4 5 6 7 8

Running Cost: 200 500 800 1200 1800 2500 3200 4000

When should the machine be replaced?

(b) The initial cost of an item is Rs 15,000 and maintenance or running costs (in Rs) for

different years are given below.

Year: 1 2 3 4 5 6 7

Running Cost: 2,500 3,000 4,000 5,000 6,500 8,000 10,000

6. (a) Use dynamic programming to solve the following problem.

Minimize Z = y

1

2

+ y

2

2

+ y

3

2

subject to the constraints

y

1

+ y

2

+ y

3

? 15 ???????????? y

1

, y

2

, y

3

? 0.

(b) What are the essential characteristics of dynamic programming problems?

7. (a) What is a game in game theory? What are the properties of a game?

(b) For the game with the following pay off matrix, determine the optimum strategies and

the value of the game.

8. (a) What are the types of inventory? Why they are maintained? Explain the various costs

related to inventory.

(b) A baking company sells cake by the pound. It makes a profit of 50 paisa a pound on

every pound sold on the day it is baked. It disposes of all cakes not sold on the date it

is baked; at a loss of 12 paisa a pound. If demand is known to be rectangular between

2,000 and 3,000 pounds, determine the optimum daily amount baked.

*****

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Code: 9F00205

MCA II Semester Regular & Supplementary Examinations August 2014

OPERATIONS RESEARCH

(For students admitted in 2009, 2010, 2011, 2012 & 2013 only)

Time: 3 hours Max. Marks: 60

Answer any FIVE questions

All questions carry equal marks

1. (a)

Discuss the importance of operations research in decision making process.

(b)

? ???? 1

+ 2 ???? 2

? 8, ???? 1

+ 2 ???? 2

? 12

Use simple method to solve the following LPP

Maximize z = ???? 1

+ 2 ???? 2

subject to

???? 1

? 2 ???? 2

? 3; ???? 1

? 0 ???????????? ???? ? 0.

(c) Use two phase simplex method to minimize Z = ???? 1

+ ???? 2

+ ???? 3

subject to the

constraints ???? 1

? 3 ???? 2

+ 4 ???? 3

= 5,

???? 1

? 2 ???? 2

? 3, 2 ???? 2

? ???? 3

? 4; ???? 1

? 0 ???????????? ???? ? 0 and

???? 3

is unrestricted.

2. (a) Use duality to solve the following LPP

Maximize Z = 2 ???? 1

+ ???? 2

subject to the constraints

???? 1

+ 2 ???? 2

? 10, ???? 1

+ ???? 3

? 6,

???? 1

? ???? 2

? 2, ???? 1

? 2 ???? 2

? 1; ???? 1

, ???? 2

? 0.

(b) Use dual simplex method to solve the LPP

Maximize Z = ?3 ???? 1

? ???? 2

subject to the constraints

???? 1

+ ???? 2

? 1, 2 ???? 1

+ 3 ???? 2

? 2; ???? 1

, ???? 2

? 0.

3. (a) Use Vogel?s approximation method to obtain an initial basic feasible solution of the

transportation problem

D E F G Available

A

B

C

?

11 13 17

16 18 14

21 24 13

14

10

10

?

250

300

400

(b)

What is an assignment problem and how do you interpret it as an L.P model?

4. (a)

Find the sequence that minimizes the total elapsed time (in hours) required to complete

the following tasks on two machines.

Task A B C D E F G H I

Machine I 2 5 4 9 6 8 7 5 4

Machine II 6 8 7 4 3 9 3 8 11

(b) Use graphic method to find the minimum elapsed total time sequence of 2 jobs and 5

machines, when we are given the following information machines.

A B C D E

2 3 4 6 2

Job I ?

Sequence:

Time in hours:

C A D E B

4 5 3 2 6

Job I ?

Sequence:

Time in hours:

Continued in page 2

Page 1 of 2

Code: 9F00205

5. (a) A firm is considering replacement of a machine, whose cost price is Rs12,200 and the

scrap value Rs 200. The running (maintenance and operating) costs in Rs are found

from experience to be as follows.

Year: 1 2 3 4 5 6 7 8

Running Cost: 200 500 800 1200 1800 2500 3200 4000

When should the machine be replaced?

(b) The initial cost of an item is Rs 15,000 and maintenance or running costs (in Rs) for

different years are given below.

Year: 1 2 3 4 5 6 7

Running Cost: 2,500 3,000 4,000 5,000 6,500 8,000 10,000

6. (a) Use dynamic programming to solve the following problem.

Minimize Z = y

1

2

+ y

2

2

+ y

3

2

subject to the constraints

y

1

+ y

2

+ y

3

? 15 ???????????? y

1

, y

2

, y

3

? 0.

(b) What are the essential characteristics of dynamic programming problems?

7. (a) What is a game in game theory? What are the properties of a game?

(b) For the game with the following pay off matrix, determine the optimum strategies and

the value of the game.

8. (a) What are the types of inventory? Why they are maintained? Explain the various costs

related to inventory.

(b) A baking company sells cake by the pound. It makes a profit of 50 paisa a pound on

every pound sold on the day it is baked. It disposes of all cakes not sold on the date it

is baked; at a loss of 12 paisa a pound. If demand is known to be rectangular between

2,000 and 3,000 pounds, determine the optimum daily amount baked.

*****

Page 2 of 2

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This post was last modified on 28 July 2020