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UNIVERSITY OF COLOMBO, SRI LANKA

UNIVERSITY OF COLOMBO SCHOOL OF COMPUTING

DEGREE OF BACHELOR OF INFORMATION TECHNOLOGY (EXTERNAL)Academic Year 2006/2007 - 2

ndYear Examination Semester 3

IT3302 Operational ResearchPART 1 - Multiple Choice Question Paper

18th

March 2007

(ONE AND A HALF HOURS)

Important Instructions :

The duration of the paper is 1 (one and a half) hours. The medium of instruction and questions is English. The paper has 30questions and 08 pages. All questions are of the MCQ (Multiple Choice Questions) type. All questions should be answered. Each question will have 5 (five) choices with one or more correct answers. All questions will carry equal marks. There will be a penalty for incorrect responses to discourage guessing. The mark given for a question will vary from 1 (All the incorrect choices

are marked & no correct choices are marked) to +1 (All the correct choices

are marked & no incorrect choices are marked).

Answers should be marked on the special answer sheet provided. Note that questions appear on both sides of the paper.

If a page is not printed, please inform the supervisor immediately.

Mark the correct choices on the question paper first and then transferthem to the given answer sheet which will be machine marked. Please

completely read and follow the instructions given on the otherside of the answer sheet before you shade your correct choices.

Non-programmable Calculators may be used.

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1) Which of the following is/are true?

(a) Operational research techniques were applied even during World War 2.(b) It is not possible to simultaneously maximize all the criteria for some management information

system.(c) Operational Research techniques are of Multi disciplinary nature.(d) In all Operational Research applications, optimal solutions can be obtained.(e) Probability distributions are used in some of the areas in Operational Research

Consider the following problem and answer questions (2), (3) and (4).

Minimize Z== 5X1 +4 X2,

subject to 3X1 + 5 X2 15,

X1+ X2 5,

X1, X2 0.

2) Which of the following (X1, X2) are feasible solutions of the problem?

(a)(5,0) (b)(5,5) (c)(0,3)(d)(0,5) (e)(3,0)

3) Which of the following is/are true?

(a) The feasible region of the problem is unbounded.(b) The feasible region of the problem is bounded.(c) There is no feasible region.(d) The feasible region of the problem is a straight line.(e) The feasible region of the problem is a single point.

4) Which of the following is/are true?

(a) There is no optimal value for the objective function.(b) The optimal value of the objective function is 15.(c) The optimal value of the objective function is 12.(d) The optimal value of the objective function is 25.(e) The optimal value of the objective function is 20.

Answer questions (5) and (6) by using the tableau of a profit maximization problem represented below in the

usual notation. (Xidenotes the number of units produced for product i=1, 2, 3 and Sis are the slack variablescorresponding to the three resourcesR1, R2and R3.)

Initial tableau

Z X1 X2 X3 S1 S2 S3 r.h.s.

1 -10 -16 -10 0 0 0 0

0 1 2 1 1 0 0 30

0 5 4 0 0 1 0 40

0 3 0 2 0 0 1 90

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5) Which of the following statements is/are true?

(a) It is most profitable to select product 2.(b) It is most profitable to select either the product 1 or the product 3.(c) Product 2 can be produced even if resource 3 is not available.(d) Maximum possible number of units of product 2 that can be produced is 15.(e) r.h.s. contains the maximum availabilities of the resources.

6) Which of the following statements is/are true?

(a) The initial solution of this problem isX1 =0, X2 =0, X3=0.(b) The initial solution of this problem isX1 =30, X2 =40, X3=90(c) Unit profit contributions ofX1 =10, X2 =16, X3=10.(d) At the initial tableau, S1 =30, S2 =40, S3 =90.(e) At the initial tableau, S1 =0, S2 =40, S3 =0.

Answer questions (7), (8), (9) and (10) using the initial tableau and the final tableau of the profitmaximization problem given below. (Xi denotes the number of units produced for product i=1,2,3.)

Initial tableau

Z X1 X2 X3 S1 S2 S3 r.h.s.

1 -8 -2 -6 0 0 0 0

0 1 2 1 1 0 0 40

0 1 4 0 0 1 0 40

0 3 0 2 0 0 1 60

Final tableau

1 0 0 1 0 5/2 190

0 3/2 0 1 0 0 30

0 -1/4 1 0 0 -1/4 5

0 2 0 0 -2 1 1 20

7) Which of the following statements is/are true?

(a) The optimum values of the dual variables are 30, 5 and 20 respectively.(b) The optimum values of the dual variables are 1, 0, 5/2 respectively.(c) The optimum values of the dual variables are 1/2, 0 and 0 respectively.(d) There is a surplus of in one dual constraint.(e) The optimum profit is 190.

8) If the profit contribution of product 1 is changed from 8 to 8 + , the possible value(s) of (8 + ) which wouldnot affect the current optimal solution is/are

(a) 9 (b) 4 (c) 8.25(d) 8.75 (e) 7

9) If the amount of resource 2 is changed by an amount , the possible value(s) of () which would not affect the

current optimal solution is/are

(a) 40 (b) 20 (c) -10(d) -25 (e) -40

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10) If the amount of resource 3 is changed by an amount , the possible value(s) of () which would not affect the

current optimal solution is/are

(a) -30 (b) -25 (c) -10(d) 10 (e) 30

11) Degeneracy in Transportation problems occur when

(a) at optimality, the total cost is 0.(b) in finding an initial solution, a row and a column requirement are simultaneously satisfied.(c) there are two or more filled cells with the same smallest negative value in a closed path for an

incoming basic variable.

(d) total supply is greater than total demand.(e) total demand is greater than the total supply.

Answer questions (12) and (13) by considering the following transportation schedule where unit costs of

transportation are given in the top left corner of each cell.

Destination S1 S2 S3 S4 AvailabilityOrigin F1 10 15 20 14 200

Origin F2 5 7 6 6 150

Origin F3 4 9 10 15 200

Demand 100 150 150 150

12) After applying the North West corner method to the above problem, the cell evaluator (C21) for route

corresponding to F2, S1 is

(a) 5 (b) 13 (c) 0(d) 7 (e) -3

13) When applying Vogels approximation method, the penalties for the F1,F2 and F3 are respectively

(a) 10,5 and 4 (b) 0, 0 and 0 (c) 5, 2 and 5(d) 4, 1 and 5 (e) 200, 150 and 200

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14) Consider the following assignment problem where three workers W1, W2 and W3 are assigned to 3 jobs J1, J2

and J3. Their estimated costs for each job are given in each cell.

W1 W2 W3

J1 5 10 8J2 7 12 10

J3 11 10 9

The best feasible assignment(s) is/are

(a)

x

x

x

(b)

x

x

x

(c)

x

x

x

(d)

x

x

x

(e)

x

x

x

15) In the shortest path algorithm, the number placed above each node represents

(a) the shortest distance from the origin to that node.

(b) the shortest distance from that node to the closest of its immediate predecessors.

(c) the shortest distance from the destination to that node.

(d) the length of the most direct route from the origin to that node.

(e) the longest path from the destination to that node.

Use the following network to answer questions 16 and 17.

16) Total length of the minimum spanning tree is

(a) 21. (b)28. (c) 19.(d) 25. (e)30.

17) Shortest path from city A to cities E and F respectively are

(a)4 and 13. (b)4 and 11. (c)10 and 12.(d)8 and 15. (e)9 and 10.

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18) Consider the following three figures.

Which of the following is/are true regarding the above figures?

(a) (i),(ii),(iii) are networks. (b) (iii) is a spanning tree.(c) (ii) is a spanning tree (d) (i) is a tree(e)

(ii) is a connected network.

19) In crashing a project network, which of the following is/are true?

(a) The first activity to be crashed is the least expensive activity on the critical path.(b) All paths with the longest time in the network must be reduced simultaneously.(c) Crashing should be done on non-critical activity.(d) First crash any activity with Total float zero.(e) First crash the activity with a positive Total float.

20) Which of the following statements is/are true for (AOA) PERT network, in general?

(a)

The network is drawn so as to indicate precedence relationships.(b) Network should not have a critical path.(c) Each node represents the beginning or end of an activity.(d) Each node consumes time.(e) Each activity consumes time.

21) With respect to a general two-person zero-sum game which of the following is/are true?

(a) The strategies of only two players are given.(b) Strategies of only one player are given.(c) There can be only two strategies.(d) Pay off table is given.(e)

Strategies of the players are not necessary at all.

1 2

3

1 2

3 4

5

1

2

34

5

i (ii (iii)

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22) Consider the following Payoff matrix of a game to a player A

The optimal solution of the game to A and B is

(a) Player A plays I and Player B plays I.(b) Player A plays II and Player B plays II.(c) Player A plays II and Player B plays III.(d) Player A plays IV and Player B plays II.(e) Player A plays IV and Player B plays III.

To answer questions (23) and (24) use the following payoff matrix of a game.

23) Optimal Strategy for player A is

(a)

0,0,

2

1,

2

1(b)

3

2,

3

1,0,0 (c)

4

3,

4

1,0,0

(d)

3

1,

3

2,0,0 (e)

0,

2

1,

2

1,0

24) The value of the game for player A is

(a) 1/3 (b) 2/3 (c) 3(d) 6/5 (e) 2

25) For a single-channel queuing model with Poisson arrivals and Exponential service times, which of thefollowing can be obtained as a result? (L-number of customers and W-waiting time of the customers, s-system

and q-queue)

(a) Ls < L q. (b) Ws < W q. (c) Wq < Ws.(d) Ls > Lq (e) Ls = Lq

Player B

I II III IV

I 8 -2 9 -3II 6 5 6 8

Player A

III -2 4 -9 5

Player B

I II III IV

I 3 2 4 2

II 3 4 2 8Player A

III 4 2 4 2

IV 2 4 0 6

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