# Loyola College B.Sc. Statistics April 2012 Operations Research Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B. Ss. DEGREE EXAMINATION – STATISTICS

SIXTH SEMESTER – April 2012

ST6604 / ST6601 – OPERATIONS RESEARCH

Date: 18-04-2012                   Dept. No.                                                            Max.:100 Marks

Time: 1.00 – 4.00

PART – A

Answer ALL questions:                                                                       (10 x 2  = 20)

1. What are the different phases of Operations Research?
2. What is a degenerate solution?
3. Give the dual for the following primal:
1. When can dual simplex method be applied to a LPP?
2. Define Two- person zero sum game.
3. Mention the two phases in the two-phase method.
4. When is there a necessity for artificial variables?
5. What are the methods used to solve a mixed strategy game?
6. What is CPM?
7. What is Minimax criterion?

PART – B

Answer any FIVE questions:                                                               (5 x 8  = 40)

1. Explain simplex method for solving an LPP.
2. The manager of an oil refinery must decide on the optimum mix of two possible blending processes of which the input and output production runs are as follows:
 Process Input Output Crude A Crude B Gasoline X Gasoline Y 1 6 4 6 9 2 5 6 5 5

The maximum amounts available of crudes A & B are 250 units and 200 units respectively. Market demand shows that at least 150 units of gasoline X and 130 units of gasoline Y must be produced. The profits per production run from process 1 and process 2 are Rs. 4 and Rs. 5 respectively. Formulate the problem for maximizing the profit.

1. What are the steps involved in solving an unbalanced transportation problem to get the optimum solution?

1. A departmental head has four subordinates and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimate of the time each man would take to perform each task, is given in the matrix below:
 Tasks Men E F G H A 18 26 17 11 B 13 28 14 26 C 38 19 18 15 D 19 26 24 10

How should the tasks be allocated, one to a man, so as to minimize the total man-hours?

1. Solve the following graphically:

Player B

Player A

1. Differentiate between Simplex method and Dual Simplex method.
2. Explain Laplace and Savage criterion in detail.
3. Explain PERT algorithm in detail.

PART – C

Answer any TWO Questions:                                                           ( 2 x 20 = 40 marks)

1. a) Explain Primal – Dual Relationship.                                                          (5)

1. b) Use Duel Simplex method to solve the following LPP.                            (15)

Minimize z = 6x1 + 7x2 + 3x3 + 5x4

Subject to

5x1 + 6x2 – 3x3 + 4x4 ≥ 12

x2 – 5x3 –  6x≥ 10

2x1 + 5x2 + x3 +   x4   ≥  8

x1, x2, x3, x4 ≥ 0

1. a) Show that for any zero-sum two-person game where there is no saddle point and for

which A’s payoff matrix is

(15)

the optimal strategies (x1, x2) and (y1, y2) for A and B respectively are determined by

What is the value of the game?

1.             20. b) What is the principle of dominance in game theory?                                          (5)

1. Find the initial basic feasible solution for the given transportation problem using:

(i)  North West Carner rule        (ii) Vogels method          (iii) Least Cost method.

 From To Available A B C I 50 30 220 1 II 90 45 170 3 III 250 200 50 4 Requirement 4 2 2

And obtain the optimal solution.

1. a) What are the rules for constructing a network diagram?                            (5)

22.  b) A project consists of eight activities with the following relevant information:

 Activity Immediate Predecessor Estimated duration (days) Optimistic Most likely Pessimistic A – 1 1 7 B – 1 4 7 C – 2 2 8 D A 1 1 1 E B 2 5 14 F C 2 5 8 G D, E 3 6 15 H F, G 1 2 3

(i)  Draw the PERT network and find out the expected project completion time.

(ii) What duration will have 95% confidence for project completion?

(iii) If the average duration for activity F increases to 14 days, what will be its effect on the expected project completion time, which will have 95% confidence?

(15)

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