# St. Joseph’s College of Commerce VI Sem Operation Research Question Paper PDF Download

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ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)
END SEMESTER EXAMINATION – MARCH/APRIL 2016
B.Com – VI Semester
C1 11 602 :OPERATION RESEARCH
Duration: 3 Hours                                                                                             Max. Marks: 100
SECTION – A
I) Answer ALL the questions.  Each carries 2 marks.                                        (10×2=20)
1. Name any four techniques of Operation Research.
2. Give any two merits of linear programming.
3. What is a key element in Simplex Method?
4. With the help of a diagram, show what is a redundant constraint?
5. How will you solve maximization case in assignment problem?
6. Give the procedure of tracing a closed loop.
7. What is independent float?
8. How do you proceed in simplex, if there is a tie for the key column?
9. What is a dummy activity?
10. Differentiate between CPM and PERT.
SECTION – B
II) Answer any FOUR questions.  Each carries 5 marks.                                      (4×5=20)
11. A  BPO requires different numbers of employees on different days of the week. Union rules state each employee must work 5 consecutive days and then receive two days off. Find the minimum number of employees needed. Formulate the problem

Mon        Tue       Wed        Thur      Fri       Sat      Sun

Staff Needed           17            13           15            19         14         16       11

12. A construction company has four large bulldozers located at four different garages. The bulldozers are to be moved to four different construction sites. The distances in miles between the bulldozers and the construction sites are given below.

 Buldozer/site A B C D 1 90 75 75 80 2 35 85 55 65 3 125 95 90 105 4 45 110 95 115

How should the bulldozers be assigned to the construction sites in order to minimize the total distance traveled?

13. Find the initial solution to the transportation problem with the help if LCM method and NWCR

 D E F G Available A 11 13 17 14 250 B 16 18 14 10 300 C 21 24 13 10 400 Required 200 225 275 250

What is unusual about the solution that is derived?

14. Draw a network diagram for the project whose activities and their predecessor relationships are given below:

Activity:         A          B         C       D         E         F         G       H

Predecessor

Activity-        –           –          –         A         B          C       D,E     F,G

15. What do you understand by the term duality? Solve the dual given below:

Min Z= 2X1 + 3 X2 + 4X3

Subject to

2X1 + 3X2 + 5X3  ≥ 2

3X1 + X2 + 7X2  = 3

X1 + 4X2 + 6X3 < 5

X1, X2,X3 > 0

16. “Operation Research is a decision science which helps management to make better decisions.” Discuss.
SECTION – C
III) Answer any THREE questions.  Each carries 15 marks.                                (3×15=45)
17. a. What are the different types of Models used in OR?  Explain in detail.
b.  The products A, B and C are produced in three machine centres X, Y and Z. Each product involves operations involves on each of the machine centres. The time required for each operation for unit amount of each product is given below:

 Products Machine Centres X Y Z A 10 7 2 B 2 3 4 C 1 2 1

There are 100, 77 and 80 hours available at machine centres X, Y and Z respectively. The profit per unit of A,B and C is Rs 12, Rs 3 and Rs 1 respectively. Formulate the LPP .                                                               (10+5)

18. Solve by Simplex Method

Maximize    Z= 3x +4y +z

Subject to constraints,

x + 2y +3z ≤ 90

2x  +y +z ≤ 60

3x + y + 2z ≤ 80

Where x,  y,  z ≥ 0

19. Five lathes are allotted to five operators (one for each). The following table gives weekly output figures (in pieces).

 Weekly output in lathe OPERATOR L1 L2 L3 L4 L5 P 20 22 27 32 36 Q 19 23 29 34 40 R 23 28 35 39 34 S 21 24 31 37 42 T 24 29 31 36 41

Profit per piece is Rs 25. Solve the assignment problem and find the maximum profit per week.

20. Solve the following transportation problem in which cell entries represent unit costs

 D1 D2 D3 AVAILABLE Q1 2 7 4 5 Q2 3 3 1 8 Q3 5 4 7 7 Q4 1 6 2 14 REQ 7 9 18 34

Apply Modi Method to test optimality and find the optimal solution.

21. An engineering project has the following activities, whose time estimates are listed below:

 Activity Estimated duration(in months) Optimistic Most Likely Pessimistic 1-2 2 2 14 1-3 2 8 14 1-4 4 4 16 2-5 2 2 2 3-5 4 10 28 4-6 4 10 16 5-6 6 12 30

1.      Draw the project network and find critical path.

2.      Find expected duration and variance for each activity.

3.      Calculate the variance and standard deviation of the project length.

4.      What is the probability that the project will be completed at least eight months earlier than the expected time?

5.      If the project due date is 38 months, what is the probability of not meeting the due date?

SECTION – D
IV) Case Study                                                                                                              (1×15=15)
22. 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 products 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 costs 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. Solve graphically.

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