OR QUESTION PAPER MCOM

1. M.COM SECOND SEMESTER (CSS) INSEM EXAMINATION JULY 2015
OPERATIONS RESEARCH
Time: 3 Hours Max Weight: 30
Section A
Answer any Five questions.
Each answer not to exceed a page.
Each question carries 1 weight
1. What is operations research?
2. Explain infeasible solution in L.P.P.
3. Describe initial basic solution.
4. Explain unbounded solution.
5. Describe MODI Method.
6. Explain VAM Method.
7. Describe Transportation problem.
8. What is an unbalanced transportation problem? ( 5 × 1 = 5 )
Section B
Answer any Five questions.
Each answer not to exceed two pages.
Each question carries 2 weight.
9. Briefly describe the different phases of operations research.
10. Explain the following terms in relation to L.P.P:
a. Feasible Solution b. Basic Feasible Solution.
11. Briefly describe the simplex method.
12. Briefly explain the advantages and disadvantages of L.P.P.
13. Explain the following briefly with examples:
a. North West Corner Rule b. Least Cost Method
14. Write down the dual of the following problem.
Maximize, Z = 4 X1 + 2 X2
Subject to, -X1 - X2 ≤ -3
-X1 + X2 ≥ -2
X1 X2 ≥ 0
15. Solve the following LPP by graphical method.
Maximize, Z = 100X1 + 40 X2

2. Subject to, 5X1 + 2 X2 ≤ 1000
3X1 + 2 X2 ≤ 900
X1 + 2 X2 ≤ 500
and X1 , X2 ≥ 0
(P.T.O)
16. Find the initial basic feasible solution by using NWCR and Matrix Minima method
Origins
Destinations
Supply1 2 3 4 5
1 16 16 13 22 17 50
2 14 14 13 19 15 60
3 19 19 20 23 25 50
4 25 0 25 0 0 50
Demand 30 20 70 30 30 210
( 5 × 2 = 10 )
Section C
Answer any three questions.
Each answer not to exceed five pages.
Each question carries 5 weight.
17. Briefly explain the important O.R techniques.
18. What do you understand by transportation model? Explain degeneracy in a transportation
problem. Describe the method to resolve it.
19. Maximize Z = 7 X1 + X2 + X3
Subject to, X1 + X2 - X 3 ≤ 10
4X1 + X2 + X 3 ≤ 20
X1 , X2 , X 3 ≥ 0
20. Find the initial basic feasible solution for the following transportation problem using
VAM.
Origins
Destinations
Supply
D1 D2 D3 D4
O1 11 13 17 14 250
O2 16 18 14 10 300

3. O3 21 24 13 10 400
Demand 200 225 275 250 950
21. A company has three plants A,B and C ; 3 warehouses X,Y and Z. the number of units
available at the plant is 60,70,80 and the demand at X,Y,Z are 50,80,80 respectively. The
unit cost of the transportation is given in the table.
X Y Z
A 8 7 3
B 3 8 9
C 11 3 5
Find the allocation so that transportation cost is minimum. (use LC Method)
22. Determine the optimal transportation plan when the unit transportation cost, demand and
supplies are given below:
Origins
Destinations
Supply
D1 D2 D3 D4
O1 6 1 9 3 70
O2 11 5 2 8 55
O3 10 12 4 7 70
Demand 85 35 50 45
(3 × 5 = 15)