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)

 

11. 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.

 

 

12. 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

 

 

13. 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

 

14. 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.

 

15. 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

 

 

16. 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)

 

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

 

18. 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

 

19. 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?

 

20. 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

 

 

21. 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)

 

22. 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.

 

 

 

 

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