# Loyola College B.Sc. Mathematics April 2009 Operations Research Question Paper PDF Download

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?

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

SECTION B

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

1. Solve the following Linear Programming Problem by graphical method

Maximize  Z = 5x1 + 8x2

Subject to:

15x1 + 10x≤  180

10x1 + 20x≤  200

15x1 + 20x≤  210

and x1, x≥ 0

1. Use simplex method to solve the following LPP

Maximize  Z = 4x1 + 10x2

Subject to:

2x1 + x≤  50

2x1 + 5x≤  100

2x1 + 3x≤  90

and x1, x≥ 0

1. 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

1. Write the algorithm for solving Assignment problem.

1. 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

1. 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.

1. 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.

1. 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)

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

Minimize  Z = x1 + x2

Subject to:

2x1 + x≥ 2

-x1 – x2 ≥ 1

and x1, x≥ 0

1. (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)

1. (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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