Operations Research

St. Joseph’s College of Commerce M.I.B. 2012 II Sem Operations Research Question Paper PDF Download

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St. joseph’s college of commerce (autonomous)

End semester examination – MARCH / april 2012

MIB – II SEMESTER 

Operations Research

Time: 3 hours                                                                                                                           Marks: 100

SECTION – A

I   Answer any SEVEN  questions. Each carries FIVE  marks.                             (7 X 5 = 35)

  1. A city police department has the minimal daily requirement for policemen.
Time of the day

(24 hours clock)

 Period Minimum number

Of policemen required
2-6 1 20
6-10 2 50
10-14 3 80
14-18 4 100
18-22 5 40
22-2 6 30

Period1 follows immediately after period6. Each policeman works for 8 consecutive hours. Formulate the linear programming problem to find the optimum daily manpower schedule. (do not solve.)

  1. Use graphical method to solve the following Linear Programming Problem.

Minimize Z= 40x + 24y

Subject to constraints

20x+50y>=4800

80x+50y>=7200

Where x, y  >=0

  1. A company has three factories at Amethi, Bagathpur and Gwalior and four distribution centers at Allahabad, Bombay, Calcutta and Delhi. With identical cost of production at three factories and only variable cost involved is transportation cost . the production at three factories is 50 tons, 60 tons and 25 tons resp. The demand at four distribution centers is 60,40,20 and 15 tons resp. The transportation costs per ton from different factories to different centers are given below. Suggest the transportation schedule using VAM method.
Distribution Center ->

Factory

 Allahabad Bombay Calcutta Delhi
Amethi 3 2 7 6
Bagathpur 7 5 2 3
Gwalior 2 5 4 5

 

  1. Briefly explain the essential features of game theory.
  2. What is an assignment problem? How does Hungarian method arrive at optimum solution. Give a brief outline.
  3. Solve the following game by dominance principle.
            Firm B à

Firm A

 

 B1 B2 B3 B4
A1 35 65 25 5
A2 30 20 15 0
A3 40 50 0 10
A4 55 60 10 15

 

  1. Construct the network diagram for the following project. Identify the critical path and project duration.
Activity Duration

(week)
1-2 5
1-3 2
2-4 3
3-6 4
4-5 2
4-6 4
5-7 7
6-7 6

 

  1. What is queuing theory? Mention some common queuing situations describing the arrivals in queue and service process.
  2. In a petropure service station, customers purchasing petrol receive a discounted car wash depending on the quality of petrol they buy. The automatic car wash bay can accommodate one car at a time and it requires a constant time of 4 mins for a wash. Cars arrive at the car wash facility at an average rate of 10 per hour.(poisson arrival). The service station manager wants to determine the average length of the queue and the average waiting time at the car wash.
  3. Discuss the role of Simulation in Operations Research.

 

 

 

 

SECTION – B

III   Answer any THREE questions. Each carries FIFTEEN marks.                     (3 X15 = 45)

  1. Solve the following LPP by problem by Simplex Method.

Maximize Z= 10x +15y +20z

Subject to

2x+4y+6Z<=24

3x+9y+6z<=30

Where x, y,z >=0

  1. Solve the following Transportation problem using NWCM  and  MODI method. What is the minimum transportation cost? Does the problem have multiple solution? ( The numbers in the table indicate the transportation cost per unit.)
Stores  ->

Warehouses

 

 P Q R Supply
A 7 4 1 35
B 3 9 8 30
C 5 4 2 35
Demand 10 60 30 100

 

  1. Pleasant Travels has one car at each of the depots P, Q, R, S, T. A customer requires a car in each city namely A,B,C,D,E. Distance in kilometers between depots and cities are given in the following distance matrix. How should the cars be assigned to customers so as to minimize the distance travelled. Solve by Hungarian method.
Depots –>

Cities

 P Q R S T
A 160 130 175 190 200
B 135 120 130 160 175
C 140 110 155 170 185
D 50 50 80 80 110
E 55 35 70 80 105

 

  1. In a market analysis, the following information was collected.
Selling

Price

 Probability Unit

Cost

 Prob Sales

Volume

 Prob Advertising

Cost

 Prob
350 0.30 300 0.40 80,000 0.15 25 Lakhs 0.25
450 0.40 350 0.25 65,000 0.45 20 Lakhs 0.25
500 0.20 400 0.15 50,000 0.30 18 Lakhs 0.25
550 0.10 450 0.20 45,000 0.10 15 lakhs 0.25

Workout the average profit and probability of profit more than Rs.50,000.

Use the following random numbers-

Selling price- 78, 43, 92, 87, 47, 83, 67, 19, 52, 05

Unit Cost- 23, 08, 28, 17, 73, 87, 28, 37, 32, 02

Sales volume- 58, 86, 62, 06, 03, 52, 19, 30, 29, 04

Advertising Cost- 21, 93, 15, 27, 06, 05, 57, 08, 62, 85

  1. What are the different types of Operations research models. Briefly explain any ten OR techniques.

Section – C

III) Compulsory Question.                                                                                        (1X20=20)

  1. a) State the differences between PERT and CPM.
  2. b) Draw the network diagram of the following Find the earliest and latest times of each event. Identify the critical path and expected project duration. Calculate all floats.
Activity Duration

(days)
1-2 10
2-3 2
2-5 6
3-4 12
3-7 9
4-5 8
4-6 5
4-8 10
5-8 4
6-7 0 ( dummy)
7-9 7
8-10 5
9-11 8
10-11 10

 

 

 

 

 

 

 

(5 + 15)

 

 

 

St. Joseph’s College of Commerce B.Com. 2013 II Sem Operations Research Question Paper PDF Download

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St. Joseph’s College Of Commerce (Autonomous)

End Semester Examination – APRIL 2013

  1. COM – VI Semester

OPERATIONS RESEARCH

Duration: 3 Hours                                                                  Max. Marks: 100

Section – A

I Answer all questions. Each carries TWO marks.                                               (10×2=20)

  1. Mention the terminologies used in formulation of a linear programming problem.
  2. Explain the techniques integer programming and replacement problems.
  3. Find the feasible region for the constraint 2x-y <=0
  4. Why is the Big M method called so? How are artificial variables used with M and why?
  5. Differentiate between an unbalanced transportation and assignment problem with the help of examples.
  6. What is a trans-shipment problem?
  7. How do you identify the optimum solution when applying Hungarian method.
  8. Mention any two differences between PERT and CPM.
  9. Describe the terms Event and Activity.
  10. Mention any four limitations of OR.

Section – B

  1. Answer any SIX questions. Each carries TEN marks.         (6×10=60)
  2. Formulate and solve by graphical method.

A firm that assembles computers is about to start production of two new type of computers. Each type will require assembly time, inspection time and storage space. The manager of the firm would like to determine the quantity of each type of computer to be produced in order to maximize the profit generated by the sales of these computer. Profit per unit of computer type1 is Rupees 600 and computer type2 is Rupees 500. The following information has been obtained by the manager after discussing with design manufacturing and marketing personnel.

Data Computer

Type 1

 Computer

Type 2

 Amount

Available

 
Assembly time

Per unit

 

Inspection time

Per unit

 

Stroage Space

 4 Hrs

 

 

2 hrs

 

 

3 cubic meters

 10 Hrs

 

 

1 Hr

 

 

3 cubis meters

 100 Hrs

 

 

22 Hrs.

 

 

39 cubic meters

 

  1. Write any two comprehensive definitions of OR. Explain the different types of Operations Research models.
  2. a) Write the dual of

Max  Z= 23x + 20y+15z

Sub to

x +2y+3z<=160

3x+10y<=230

8y-10z>=175

X<=50

Where x, y,z>=0

  1. b) Solve by  Big M method

Max Z= 10x + 12y

Subject to,

X+ y = 5

X >= 2

Y<= 4

Where x, y >=0                                                                                                  (4 + 6)

 

  1. The estimated sales (tons) per month in four different cities by five different managers is given below:
Managers Cities
A B C D
P 13 15 12 14
Q 12 14 10 12
R 16 18 14 14
S 15 15 13 13
T 14 15 14 12
  1. a) Find out the assignment of cities to managers in order to maximize sales.
  2. b) The management wants to send one of the managers for training for improving sales performace. Who should be sent for such a training without loosing sales?

 

  1. Hindusthan construction company needs 3, 3, 4 and 5 million cubic feet of fill at four earthern damsites in Punjab. It can transfer the fill from three mounds A, B and C where 2, 6 and 7 cubic million cubic feet are available respectively. Costs of transporting one million cubic feet of fill from mound to the four sites in lakhs are:
Damsites ->

Mounds

 I II III IV
A 15 10 17 18
B 16 13 12 13
C 12 17 20 11

Find initial solution to the following transportation problem using

  1. NWCM b) LCM  c) Vogel’s approximation method

Find the cost of transportation in each case. Which method gives the least cost initial solution?

  1. An officer has worked on the transportation schedule from his experience.
Destination ->

Source

 1 2 3 Availability
A 10 7 8 45
B 15 12 9 15
C 7 8 12 40
Requirement 25 55 30  

Solution given by the officer is:

Source Destination Units transported
A

A

B

C

C

Dummy

 2

3

2

1

2

3

 25

20

15

25

15

10
  1. Is the solution given by the officer optimum ?
  2. If not find the best solution to the problem.
  3. a) Draw the network diagram for the following.
  4. b) Apply forward pass, backward pass and calculate earliest and latest timings of each activity
  5. c) Calculate total float and identify the critical path and duration of the project.
Activity Immediate

Predcessor

 

 Duration

(weeks)
A

B

C

D

E

F

G

 –

–

–

A

B

C

D,E

 2

4

3

1

6

5

7

 

  1. Solve by Simplex Method

Maximize Z= 6x + 8y

Subject to,

5x + 10y<=60

4x + 4y <=40

Where x,y >=0

  1. What are the important characteristics of OR? Explain the phases of solving a problem using Operations Research?

Section – C

III) Compulsory Question                                                                                          (1 X 20=20)

  1. IV) The following details of a project are known.
  2. Draw the network diagram     (4)
  3. Find the expected time and variance of activities.   (3)
  4. Find the earliest and latest starting and finishing time of each activity.(4)
  5. Find total float, free float and independent float of all non critical activities.(3)
  6. Identify the critical path and the project duration? (2)

 

  1. What is the probability that the project may be completed in (3)
  2. i) 25 days ii) 20 days    iii) 30 days
  3. g) If you want to be 99% sure of completing the project what should be the deadline? (1)

 

Activity To Tm Tp
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 2 5 8

 

 

St. Joseph’s College of Commerce BBM 2013 V Sem Operations Research Question Paper PDF Download

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1
ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)
END SEMESTER EXAMINATION – OCTOBER 2013
BBM – V SEMESTER
OPERATIONS RESEARCH
Duration: 3 HOURS Max. Marks: 100
SECTION – A
I. Answer ALL the following questions. (2 marks each) (10×2=20)
1. “Operations Research is a scientific and systematic problem solving tool in every field”-
with reference to this statement bring out the Interdisciplinary feature of operations
research.
2. Introduce suitable variables for the following expressions:
a. 2x+3y=20 b. 4a+5b >= 6 c. 20p+30q<= 55 d. 7x+4y >=10
3. State any four techniques of Operations Research.
4. What is the coefficient introduced inthe objective function in case of slack and surplus
variables? Give an example.
5. For the given equation 2x + 3y <= 6 plot and identify where the feasible region lies.
6. Explain Unbalanced Assignment Problem.
7. Mention the three techniques of finding the Initial Basic Feasible Solution.
8. Define utility in decision theory.
9. Show with help of a diagram Head Event and Tail Event for an activity.
10. In case of Transportation problem, what is meant by degeneracy and non- degeneracy
solution.
SECTION – B
II. Answer ANY FOUR of the following questions (4×5= 20)
11. An Electric Appliance Company produces two products: Refrigerators and Ranges.
Production takes place in two separate departments I and II. Refrigerators are produced
in department I and Ranges in department II. The company’s two products are sold on a
weekly basis. The weekly production cannot exceed 25 Refrigerators and 35 Ranges. The
company regularly employs a total of 60 workers in the two departments. A Refrigerator
requires 2 man-weeks labour while a Range requires 1 man-week labour. A Refrigerator
contributes a profit of Rs. 60 and a Range contributes a profit of Rs. 40. How many units
of refrigerators and ranges should the company produce to realize the maximum profit?
Formulate the above as an LPP.
12. “O.R. is the application of scientific methods to problem arising from operations
involving integrated system of men, machines and materials.”—with reference to this
bring out the various features of Operations Research.
13. Obtain the Primal and Dual of the following LPP and state how many constraints and
variables are formed after duality.
Max Z = 3x + 4y + 2z
Subject to constraints:
2
x + y <= 8
y + z <= 15
8x + 2y <= 2
x + y – z <= 12
2x + 2y + z <= 22
4x + 3y <= 21
z <= 3
Where x, y, z >= 0
14. International Oil Company has three Refineries and four Depots. Transportation costs
per ton and requirements are given below:
D1 D2 D3 D4 Capacity
P1 5 7 13 10 700
P2 8 6 14 13 500
P3 12 10 9 11 800
Requirement 300 600 700 400 ?
Determine the Initial Basic feasible Solution using NWCM.
15. The following represents the various activities of a project:
Activity Preceding Activity
A —
B —
C A
D A
E B
F C
G D,E
Draw a network diagram for the above and show the activities after numbering the events.
16. “Decision- maker is a person who is responsible for making decisions. Decisions are
made under various situations”— In this context, explain the various decision – making
environments.
SECTION – C
III. Answer ANY THREE of the following questions (3×15=45)
17. By using the graphical method solve the following LPP:
Max Z = 3a + 4b
Subject to constraints:
5a + 4b <= 200
3a + 5b <= 150
5a + 4b >= 100
8a + 4b >= 80
Where, a, b >= 0. Also show the necessary verification workings.
3
18. Solve the following LPP using Simplex Method:
Max Z = 3x + 2y + 5z
Subject to constraints:
x + 2y + z <= 430
3x + 2z <= 460
x + 4y <= 420
Non – Negativity Restriction = x, y, z >= 0
19. The owner of a small machine shop has four mechanics available to assign jobs for the
day. Five jobs offered with expected profit for each mechanic on each jobs, which are as
follows:
Mechanics \ Jobs A B C D E
M1 62 78 50 111 82
M2 71 84 61 73 59
M3 87 92 111 72 81
M4 48 64 87 77 80
By using the Hungarian Method, find the assignment of mechanics to the job that will
result in Maximum Profit. Which job should be declined?
20. (a)“A model is a representation of the reality. Most of our thinking of operation research
in business take place in the context of models”— with reference to this statement briefly
explain the various types of models used in operations research. (10 marks)
(b) Write a short note on Decision Tree Analysis (5marks)
21. Solve the following Transportation Problem using VAM to arrive at the IBFS and also
TEST IT FOR OPTIMALITY using MODI method.
From\ To I II III IV SUPPLY
A 15 10 17 18 2
B 16 13 12 13 6
C 12 17 20 11 7
DEMAND 3 3 4 5 ?
SECTION -D
IV. Answer the following question (COMPULSORY) (1×15=15)
22. St. Joseph’s College of Commerce Final year BBM students had taken up a project work
in the field of construction. BBM students of SJCC were known for their creativity and
were also very confident in taking up the project because they had studied Operations
Research as one of the subjects. The project was to be completed within a stipulated
period of time. Lot of pressures were put on the students as there were in their final year.
They divided the entire project into different activities and events so that they could
reduce their project duration and complete on time. The following were the details of the
project:
4
ACTIVITY to (weeks) tm (weeks) tp (weeks)
1-2 1 1 7
1-3 1 4 7
1-4 2 2 8
2-5 1 1 1
3-5 2 5 14
4-6 2 5 8
5-6 3 6 15
With the details available keeping in mind you are one among the final year BBM student,
present the Network Project Report Plan using the Network Analysis techniques for the
following:
a. Draw the project network.
b. Determine the Expected Project Length and identify all the paths.
c. Show Early Start, Early Finish, Late Start, and Late Finish time of the project and
Total Float.
d. Compute the variance and standard deviation of the project.
e. What is the probability that the project will be completed within 19 weeks?

St. Joseph’s College of Commerce B.Com. 2014 VI Sem Operations Research Question Paper PDF Download

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  1. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

END SEMESTER EXAMINATION – MARCH / APRIL 2014

B.COM – VI SEMESTER

 OPERATIONS RESEARCH

Max. Time : 3 Hrs.                                                                                                         Max. Marks : 100

Section – A

  1. Answer ALL the following questions. Each carries 2 marks.               (10 x 2 =20)

 

  1. Define Operation Research.
  2. Write any two limitations of Operations Research.
  3. What are Mathematical Models? Give an example.
  4. Give the meaning of a dummy activity?
  5. What do you mean by Integer Programming?
  6. Any two disadvantages of Northwest Corner Rule.
  7. What is a Project? Give two examples.
  8. Write any two differences between PERT and CPM.
  9. Any two advantages of Linear Programming Model.
  10. Write any two differences between Surplus Variables and Slack Variables.

 

Section – B

  1. II) Answer any FOUR Each carries 5 marks. (4×5=20)

 

  1. State whether the following  statements are TRUE Or FALSE by giving reasons for the same.

 

  1. If the optimal simplex table contains artificial variables also, then it is a LPP with no feasible solution.
  2. Surplus variable will have +1 as it’s co-efficient in the constraint.
  3. In an assignment problem, if the number of rows is not equal to the number of columns, then it is called balanced assignment problem.
  4. Loop should commence from and end in the selected highest positive cell.
  5. Operations Research is an interdisciplinary team approach.

 

 

  1. Find the Initial Basic Feasible Solution to minimize the transportation cost under Vogel’s Approximation Method:

Transportation Cost structure is given below:

 

Supply Points Destinations
D1 D2 D3 D4 Supply
P1 19 30 50 12 7
P2 70 30 40 60 10
P3 40 10 60 20 18
Demand 5 8 7 15

 

 

  1. Find the optimal assignment for the following cost matrix:

 

Salesmen Areas
A1 A2 A3 A4
S1 11 17 8 16
S2 9 7 12 10
S3 13 16 15 12
S4 14 10 12 11

 

  1. A rubber Co. is engaged in producing three different types of tyres A, B and C. These three different tyres are produced at the Company’s two different production capacities.  In a normal 8 hours working day, Plant 1 produces 100, 200 and 200 types of tyres of A, B and C respectively.  Plant 2 produces 120, 120 and 400 type of tyres of A, B and C respectively.  The monthly demand of A, B and C is 5000, 6000 and 14,000 tyres respectively.  The daily cost of operation of Plant 1, and Plant 2 is Rs. 5,000 and Rs. 7,000 respectively.

Formulate the problem as a Linear Programming Model in order to minimum no. of days of operation per month at two different plants to minimize the total cost while meeting the demand.

 

  1. Draw a network based on the following information and state its critical path and the duration of the project.

 

Activity Immediate Predecessors Duration in days
A None 3
B None 5
C A 1
D B 4
E C,D 2
F C,D 3
G E 7
H F 6

 

 

  1. Write the dual of the following linear programming problem:

Min. Z = 5×1 – 6×2 + 4×3

Subject to:

3×1 + 4×2 + 6×3 >= 9

x1 + 3×2 + 2×3 >= 5

7×1 – 2×2 – x3 <= 10

x1 – 2×2 + 4×3 >= 4

2×1 + 5×2 – 3×3 >=3

Where   x1, x2 and x3 >= 0

 

 

 

 

Section – C

 

III) Answer any Three questions.  Each carries 15 marks.                                (3×15=45)

 

  1. What do you mean by Operations Research? Give any five features of Operations Research.  Also state its scope in the field of:
  2. a) Agriculture b) Production c) Marketing           and       d) Research and Development.

 

  1. Solve graphically:

Min. Z = 6×1 + 14×2

Subject to:

5×1 + 4×2 >= 60

3×1 + 7×2 <= 84

x1 + 2×2 > = 18

where,   x1 & x2 >= 0

 

  1. The Captain of the Playwell Cricket team has to allot five middle order batting positions to five batsmen. The average runs scored by each batsman at these positions are as follows:
Batsman Batting Positions
I II III IV V
P 40 40 35 25 50
Q 42 30 16 25 27
R 50 48 40 60 50
S 20 19 20 18 25
T 58 60 59 55 53

 

You are required to find:

  1. The assignment of batsmen to positions, which would give the maximum number of runs.
  2. What will be the total runs scored if Batsman T wants only the III position?

 

  1. Solve the following LPP by Simplex Method:

Max. Z = 4×1 + 5×2 – 3×3

Subject to:

x1 + x2 + x3 = 10

x1 – x2 >= 1

2×1 + 3×2 + x3 <= 30

Where, x1 , x2 and x3 >= 0

 

 

  1. The monthly maintenance work in a machine shop consists of 10 steps. The inter-relationship between them are identified by event numbers which are as follows:

 

Event No. 1-2 2-3 2-4 3-5 3-6 4-6 4-7 5-8 6-8 7-8
No. of Days 3 5 8 4 2 9 3 12 10 6

 

Required:

  1. Draw a network.
  2. Identify critical activities and critical path.
  3. What will be the project completion time?
  4. Compute Total Float, Free Float and Independent Float.

 

Section – D

  1. IV) Compulsory Question:  (1 x 15=15)

 

  1. Given below is the table taken from the solution process of transportation problem.
Factories Destinations Availability
 1  2 3 4
A       5000                         5,000
10   8   7   12  
B           4500   1500                 6,000
12   13   6   10  
C   7000   500       1500                 9,000
8   10   12   14  
Demand                      7,000                              5,500                              4,500                              3,000  

 

Answer the following questions:

  1. Is this solution feasible? If yes, give reason.
  2. Is this solution degenerate? State the reason for your answer.
  3. Is this solution optimal? Use Modi’s Method to test the Optimality.
  4. If the solution is not optimal, find the optimal solution.
  5. Does the problem have any alternate optimal solutions? Give reason.

 

 

 

 

St. Joseph’s College of Commerce B.B.M. 2014 V Sem Operations Research Question Paper PDF Download

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  1. JOSEPHS COLLEGE OF COMMERCE (AUTONOMOUS)

END SEMESTER EXAMINATION – OCTOBER 2014

B.B.M. – V SEMESTER

 OPERATIONS RESEARCH

Duration: 3 Hours                                                                                       Max. Marks: 100

SECTION – A

 

  1. Answer ALL the questions. Each carries 2 marks.                                       (10 x2 =20)

 

  1. Give the meaning of Operations Research.
  2. In the context of transportation model, explain degeneracy and non-degeneracy.
  3. Describe the assignment problem giving suitable example. Give two areas of its applications.
  4. Explain the utility concept in case of decision theory.
  5. Introduce suitable variables for the expression to convert into standard form for simplex method  (a) 2a+3b<= 5       (b) 5x+4y+3z>=10
  6. What is an Unbalanced Assignment Model? How is it solved by Hungarian Method?
  7. Bring out any two significant differences between PERT and CPM.
  8. Discuss unbounded solution and feasible solution in case of graphical method of solving LPP.
  9. What are floats or slack in a network diagram?
  10. “OR is an inter-disciplinary team approach”- Explain.

 

SECTION – B

 

  1. Answer any FOUR Each carries 5 marks.                               (4×5=20)

11.Draw the complete CPM network according to the following activities:

DURATION (weeks) STARTS AT EVENT ENDS AT EVENT
5 1 2
6 1 3
3 1 4
4 2 3
6 2 5
7 3 4
4 3 5
8 4 5

Determine the Critical Path.

 

  1. Solve the following problem by Least Cost Method and determine Initial Basic Feasible Solution.
From/  To D E F Supply
A 6 4 1 50
B 3 8 7 40
C 4 4 2 60
Demand 20 95 35 ?

 

  1. “OR has certain limitations. However, these limitations are mostly related to the problems of model building and time and money factors. ”—In this context briefly explain the demerits of OR with regard to application rather than it practical utility.

 

  1. Consider the following problem of assigning five jobs to five persons. The assignment costs are given below:

 

PERSON/JOBS I II III IV V
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

Determine the optimum Assignment Schedule and Minimum Cost.

Note: Assignment cost is in thousands.

 

  1. A farmer is engaged in breeding pigs. The pigs are fed on various products grown on the farm. Because of the need to ensure nutrient constituents, it is necessary to buy additional one or two products, which we shall call A and B. the nutrient constituents (vitamins and proteins) in each of the product are given below:

 

nutrient constituents nutrient in the product minimum requirement of nutrient constituents
  A B  
X 36 6 108
Y 3 12 36
Z 20 10 100

Product A cost Rs. 20 per unit and Product B costs Rs. 40 per unit. Determine how much of products A and B must be purchased so as to provide the pigs nutrients not less than the minimum required, at the lowest possible cost. Formulate it as LPP.

 

  1. Write the dual of the following LPP and state the no. of decision variables and constraints in primal and dual of the problem:

Minimize Z= 5x1 – 6x2 + 4x3

Subject to Constraints:

3x1 + 4x2 + 6x3 >= 9

x1 + 3x2 + 2x3 >= 5

7x1 – 2 x2 – x3 <= 10

x1 – 2x2 + 4x3 >= 4

2x1 + 5x2 – 3x3 >= 3

 

Non- negativity constraints:

x1, x2, x3 >= 0

 

 

 

SECTION – C

 

III)      Answer any THREE questions.    Each carries 15 marks.                    (3×15=45)

 

  1. Use the graphical method to solve the following LPP.

Maximize Z = 5x1 + 2x2

Subject to constraints:

2x1 + 3x2 <= 150

3x1           <= 150

5x2           <= 200

Where, x1, x2 & x3 >=0

 

 

18.Given below the transportation problem, Answer the following questions:

Factories/Warehouse I II III IV Availability
A 10 8 7 12 5000
B 12 13 6 10 6000
C 8 10 12 14 9000
Demand 7000 5500 4500 3000 ?
  1. Find the IBFS using VAM and is this solution feasible? (5marks)
  2. Is this solution degenerate?                     (1 mark)
  3. Is this solution optimal? If not find the optimal solution using MODI method.                                                  (9marks)

 

  1. A marketing manager has five salesmen and five sales districts. Considering the capabilities of the salesmen and nature of districts, the marketing managerestimates that sales per month (in hundred rupees) for each salesman in each district would be as follows:
Salesmen Districts
A B C D E
I 32 38 40 28 40
II 40 24 28 21 36
III 41 27 33 30 37
IV 22 38 41 36 36
V 29 33 40 35 39

Find the assignment of salesmen to districts that will result in maximum sales using Hungarian method.

 

  1. 20. Solve using Big-M method for the following LPP.

Min Z: 500x + 200y

Subject to constraints:

3x + 2y <= 90

x >= 10

y >= 10

Non-negativity constraints:

x, y >= 0

 

 

 

21.(a)“Most of the OR techniques are simple and can be used without much mathematical complications. Hence, managers at various levels need not be scared of using these techniques”—In this context explain briefly the various techniques used in OR for taking decisions.                                        (10 marks)

 

(b) Write a short note on Decision Tree Analysis with a diagrammatic representation.                                                                                            (5 marks)

 

SECTION – D

 

  1. IV) Case study- Compulsory questions.      (15 marks)

 

  1. A construction company is preparing a PERT network for laying the foundation of a new art museum. Given the following set of activities, their predecessor requirements and three time estimates of completion time:
Activities pessimistic time most likely time optimistic time
1-2 7 1 1
1-3 7 4 1
1-4 8 2 2
2-5 1 1 1
3-5 14 5 2
4-6 8 5 2
5-6 15 6 3
  • Determine the expected time and variance for each activity.
  • Draw the network and determine the project duration and critical path.
  • Determine earliest time and latest time and total float for the same network.
  • What is the probability that the project is completed 4 weeks earlier than expected?
  • If the target time is 18 weeks what is the probability of meeting the target?

 

 

 

 

 

St. Joseph’s College of Commerce B.B.A. 2015 Operations Research Question Paper PDF Download

by
  1. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

END SEMESTER EXAMINATION – SEPT/OCT. 2015

B.B.M. – V SEMESTER

M1 11 504: OPERATIONS RESEARCH

Duration: 3 Hours                                                                                         Max. Marks: 100

 

Section – A

  1. Answer ALL the questions. Each carries 2 marks.                                         (2×10=20)

1)  Classify operation research models based on:

  1. a) Time
  2. b) Degree of certainity

 

2)  Mention any Four Features of Operation Research.

 

3) With reference to linear programming problems explain the following terms:

  1. a) Infeasible solution
  2. b) Redundant constraint

 

4) List any four areas of LPP application.

 

5) Introduce appropriate variables (slack, surplus or artificial) and convert the following    to equations

  1. a) 3x + 5y < 15

b )4x + 3y >6

 

6)  Distinguish between PERT and CPM.

 

7)  A project manager has to manage various projects. For each project given below, you     are required to advise him whether to use PERT or CPM and briefly state the reason ?

 

  1. Project K is yet to begin. The manager had recently successfully handled similar projects. He is able to break down the project into smaller modules and knows when he may comfortably finish each module.
  2. Project M is new to the manager. He has never handled such a project he can break up the project into smaller modules, but even then, he is not sure of their exact times.

 

8)  How will you treat a Transportation problem with a Maximization objective?

 

9)  In case of an Unbalanced Assignment Matrix, what step is required to balance it?

 

 

10) Point out the errors in the network given below, going by the usual conventions while drawing a network to use CPM.

 

 

 

SECTION – B

  1. II) Answer any FOUR questions. Each carries 5 marks.                                 (4×5=20)

 

  1. Woods Product Ltd. currently produces two major products, tables and chairs. When sold, each chair yields a profit of `35 and table   `45.  An analysis of the production work sheets reveals the following manufacturing data:
Product Man hrs. per unit Machine hrs. per unit
Chair 5 0.8
Table 8 1.2
Time available during the year 800 Man hours 485 Machine hours

 

The company has a minimum demand for 50 chairs and a maximum demand for 25 tables during year 2013.  Construct an appropriate linear programme for maximizing the profit of Woods Product Ltd.

 

  1. B. Sahni chartered accountant firm has four chartered accountants each of whom can be assigned any of the three audit assignments. Because of the varying work experience of the chartered accountants, the net surplus (professional fees minus expenses to be incurred by the CA firm) varies as under:
  Audit Assignments
Chartered Accountant W X Y
A 65 78 83
B 85 52 59
C 83 56 69
D 49 80 85

 

You are required to find the maximum net surplus which can be obtained.

 

  1. a) Solve the following transportation problem by
  2. North west corner Rule (NWCR)
  3. Least Cost Method (LCM)
               D

W

 D1 D2 D3 D4 D5 Availability
W1 3 4 6 8 8 20
W2 2 10 0 5 8 30
W3 7 11 20 40 3 15
W4 1 0 9 14 16 13
Required 40 6 8 18 6 78

 

  1. Is the cost of transportation reduced through LCM in comparison to the  NWCR,  if so to what extent?

 

  1. Find the Dual of the following problem:

Maximize      Z = 30 x1   +  20 x2

Subject to constraints:  -x1 – x2 > -8

-6x1 – 4x2 < – 12

5x1 + 8x2 = 20

x1, x2 >0

 

  1. What is meant by decision tree analysis? Explain the types of decision making environment?

 

  1. The following table gives the activities in a construction project and the time duration of each activity:
Activity Preceding activity Normal time (days)
A – 16
B – 20
C A 8
D A 10
E B,C 6
F D,E 12

Required :

  1. Draw the activity network of the project.
  2. Find the critical path.

 

Section- C

  1. II) Answer any THREE questions. Each carries 15 marks.                                 (3×15=45)

 

  1. Solve the following LPP by using the Big – M method

Max Z=10x+12y

Subject to constraints

x + y=5

x > 2

y < 4

where    x, y >0

  1. A car hire company has one car at each of the five depots M,N, O, P & Q. A customer in each of the five towns A,B,C,D,&E, requires a car. the distance (in miles)between the depots (origins) and the towns (destinations) where the customers are, are given in the following distance matrix.
    M N O P Q
 

 

Person

  A 160 130 175 190 200
 B 135 120 130 160 175
C 140 110 155 170 185
D 50 50 80 80 110
E 55 35 70 80 105

How should the cars be assigned to the customers so as to minimize the distance travelled. Solve the above Assignment problem by using  the Hungarian Method.

 

  1. A) A Small project is composed of seven activities, whose times estimates (in days) are listed below. Activities are identified by their beginning (i) and ending (j) node numbers.
Activity (i-j) 1-2 1-3 1-4 2-5 3-5 4-6 5-6  
Duration to 2 2 4 2 4 4 6  
Duration  tm 2 8 4 2 10 10 12  
Duration tp 14 14 16 2 28 16 30  
  1. Draw the project network
  2. Find the Expected Duration and Variance for each activity. What is the expected project length?
  3. If the project due date is 38 days, what is the probability of meeting the due date?

 

19.B) Given that operation research represents an integrated framework to help make decisions, it is important to have a clear understanding of this framework so that it can be applied to a generic problem.  In light of the above statement examine the methodology / steps involved in solving an Operation Research problem.

(10+5)

  1. The following linear program is presented to you:
Objective  :Maximize Z=30X +45Y

Subjective to :  (i)2X+3Y, < 1,440

(ii) 9X+12Y > 2,160

(iii) 3x + 4y > 1080

(iv) x,y >0.

 Required:

Draw the Graph taking quantities of x and y in the respective axes in steps of 60 units (scale 1 cm = 60units) and solve the following LPP

Determine the optimality and offer your comments on the solution and the constraints

21) The activities in respect of a maintenance project are as below:

Activity 1-2 1-3 1-4 2-5 3-6 3-7 4-7 5-8 6-8 7-9 8-9
Months 2 2 1 4 5 8 3 1 4 5 3
  1. Draw the project network.
  2. Find the Critical Path and Duration of the project.
  3. Perform the forward and backward pass computations and derive the EST, EFT, LST and LFT for each event/activity.
  4. Determine Total Float, Free Float and Independent Float.

SECTION –D

  1. IV) Case Study – Compulsory question.          (1×15=15)
  2. A company has four factories F1, F2, F3 & F4 manufacturing the same product. Production and raw material cost differ from factory to factory and given in the following table.  The transportation cost from the factories to the sales depots S1, S2 & S3 are also given.  The costs, total requirement  at each depot and also the product capacity at each factory are also stated below.
  F1 F2 F3 F4 Requirement
S1 19 30 50 10 7
S2 70 30 40 60 9
S3 40 8 70 20 18
Capacity 5 8 7 14 34
  1. Obtain an IBFS to minimize the costs of the following transportation problem by VAM:
  2. Test the optimality of the solution thus obtained using the MODI method.
  3. Is the solution degenerate?
  4. If need be optimize the solution.

 

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