LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – MATHEMATICS

ZA 31

FIFTH SEMESTER – April 2009

MT 5507 / 5504 – OPERATIONS RESEARCH

 

 

 

Date & Time: 17/04/2009 / 9:00 – 12:00    Dept. No.                                                       Max. : 100 Marks

 

 

SECTION A

Answer  ALL  Questions                                                                               (10 x 2 = 20)

 

1. Write down any two uses of Operations Research.
2. Define Slack variables.
3. Which is the necessary and sufficient condition for the transportation problem to have

a feasible solution?

4. Describe a traveling salesman problem.
5. What is meant by mixed strategy?
6. What is the value of the game?
7. Define Total float
8. Explain: Minimal Spanning tree problem?
9. Give any two reasons for maintaining inventory
10. Define Recorder level.

 

SECTION B

Answer ANY FIVE Questions.                                                                     (5 x 8 = 40)

 

11. Solve the following Linear Programming Problem by graphical method

Maximize  Z = 5x₁ + 8x₂

Subject to:

15x₁ + 10x₂  ≤  180

10x₁ + 20x₂  ≤  200

15x₁ + 20x₂  ≤  210

and x₁, x₂  ≥ 0

12. Use simplex method to solve the following LPP

Maximize  Z = 4x₁ + 10x₂

Subject to:

2x₁ + x₂  ≤  50

2x₁ + 5x₂  ≤  100

2x₁ + 3x₂  ≤  90

and x₁, x₂  ≥ 0

 

13. Find the initial basic feasible solution for the following transportation problem

	D1	D2	D3	D4	Supply
S1	21	16	25	13	11
S2	17	18	14	23	13
S3	32	27	18	41	19
Demand	6	10	12	15

 

 

 

 

 

 

 

14. Write the algorithm for solving Assignment problem.

 

15. Solve the following game using dominance property.

 

	I	II	III	Row mini.
I	1	7	2	1
II	6	2	7	2
III	6	1	6	1
Column max.	6	7	7

 

 

 

 

 

 

16. Draw the network for the project whose activities with their predecessor relationships

are given below:

A, C, D can start simultaneously; E >B, C;  F, G >D;  H, I > E ,F ; J >I, G ;

K > H; B > A.

 

17. The annual demand of a product is 10,000 units, each unit cost Rs.100 if orders

placed in quantities below 200 units but for orders of 200 or above, the price is Rs.95,

the annual inventory holding cost is 10% of the value of the item, and the ordering

cost is Rs.5 per order. Find the economic lot size.

 

18. The demand for an item in a company is 18,000 units per year and the company can

produce the item at a rate of 3000 per month. The cost of one set up is Rs. 500 and

the holding cost of one unit per month is 15 paise. The shortage cost of one unit is

Rs. 20 per month. Determine the optimum manufacturing quantity and the number

of shortage. Also determine the manufacturing time and time between setups.

 

 

SECTION C

Answer ANY TWO Questions.                                                                      (2 x 20 = 40)

19. Solve the following Linear Programming Problem by Dual Simplex method

Minimize  Z = x₁ + x₂

Subject to:

2x₁ + x₂  ≥ 2

-x₁ – x₂ ≥ 1

and x₁, x₂  ≥ 0

 

20. (a) Solve the following transportation problem using Least Cost Method to find the

Initial Basic Feasible solution.

 

	A1	A2	A3	A4	A5	Supply
B1	4	1	2	6	9	100
B2	1	4	7	3	8	120
B3	7	2	4	7	7	120
Demand	40	20	70	90	90

.

 

 

 

(b)Solve the following traveling sales man problem

 

	M1	M2	M3	M4	M5
J1	9	22	58	11	19
J2	43	78	72	50	63
J3	41	28	91	37	45
J4	74	42	27	49	39
J5	36	11	57	22	25

(10 + 10)

21. (a) Solve the following game graphically

	B1	B2	B3	B4
A1	1	0	4	-1
A2	-1	1	2	5

 

(b) In a game of matching points with 2 players suppose A wins one unit value when

there are 2 heads, wins nothing when there are 2 tails, and loses  ½ unit value when

there are 1 head and 1 tail. Determine the pay-off matrix, the best strategy for each

player and the value of the game.                                                        (10+10)

 

22    (a) Draw the network, determine the critical path , project duration and the total float for the

following activities .

 

Activity	1-2	2-3	3-4	3-7	4-5	4-7	5-6	6-7
Duration	3	4	4	4	2	2	3	2

 

(b) ABC manufacturing company purchases 9,000 parts of a machine for its annual

requirement, ordering one month’s usage at a time. Each part costs Rs.20.

The ordering cost per order is Rs.15, and the carrying charges are 15% of the

average inventory per year.

You have been asked to suggest a more economical purchasing policy for the

company. What advice would you offer and how much would it save the company

per year?                                                                                  (10+10)

 

 

 

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