Tamil Nadu Open University (TNOU) 2009 B.Sc Mathematics Bms-09 linear programming and operations research , - Question Paper
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UG-472 BMS-09B.Sc. DEGREE EXAMINATION -JANUARY 2009.
(AY - 2005-06 and CY - 2006 batches only)
Third Year
Mathematics
LINEAR PROGRAMMING AND OPERATIONS RESEARCH
Time : 3 hours Maximum marks : 75
SECTION A (5 x 5 = 25 marks)
Answer any FIVE questions.
1. Write the following linear programming problem in standard form.
Minimize Z - 2x1 - 3x2 + x3
Subject to - xx + 3x2 < -5 x1 + 2x2 + x3 < 6 x1 + x2 + x3 > -8 x1; x2, x3 > 0.
2. Explain the term artificial variables and its use in linear programming.
3. Explain the primal-dual relationship.
4. Give the mathematical formulation of an assignment problem. How does it differ from a transportation problem?
5. Obtain an initial basic feasible solution to the following transportation problem by using North West Corner Rule.
|
D |
E |
F |
G |
Available | |
|
A |
11 |
13 |
17 |
14 |
250 |
|
B |
16 |
18 |
14 |
10 |
300 |
|
C |
21 |
24 |
13 |
10 |
400 |
Requirement 200 225 275 250
6. Explain the following terms in inventory management.
(a) Carrying cost
(b) Shortage cost.
7. What is replacement? Describe some important replacement situations.
Answer any FIVE questions.
9. Let S= ,x2....xn Jz Rn . Then prove that the set of all convex combinations of x2....xn is a convex set in Rn.
10. Use simplex method to solve the following LPP : Maximize Z - 3x, + 2x2
Subject to x1 - x2 < 1 3x1 - 2x2 < 6 xv x2 > 0.
11. Solve the following assignment problem which minimises the total man hours.
A 1 /18
C
17 14
18 24
B
26
28
19
26
D
11
26
15
10
Jobs
13
38
19
12. Solve the following unbalanced transportation problem.
To
|
From |
|
800 500 900 |
13. Neon lights in an industrial park are replaced at the rate of 100 units per day. The physical plant orders the neon lights periodically. It costs Rs. 100 to initiate a purchase order. A neon light kept in storage is estimated to cost about Re. 02 per day. The lead time between placing and receiving an order is 12 days. Determine the optimum inventory policy for ordering the neon lights.
14. The cost of a machine is Rs. 6,100 and its scrap value is only Rs. 100. The maintenance costs are found from experience to be :
Year : 1 2 3 4 5 6 7 8
Maintenance
cost : 100 250 400 600 900 1250 1600 2000
When should the machine be replaced?
15. Find out the optimum strategies for the following 2x2 game without saddle point.
|
B | |
|
5 1 | |
|
A |
.3 4 |
16. In the model {V/FIFO findPn
4 UG-472
|
Attachment: |
| Earning: Approval pending. |
