Model Question Paper Subject Code: MC0079 Subject Name: Computer Based Optimization methods Credits: 4

Marks: 140 Part A (One mark questions)

1. The phase in operations research which consists of making recommendations for the decision process usually by those who first posed the problem is known as A) Action phase B) Recommend phase C) Research phase D) Judgement phase

2. The ……………. are the unknowns to be determined from the solution of the model. A) Arithmetic variables B) Algebriac variables C) Decision variables D) Logical variables

3. The …………………. is a class of mathematical programming in which the functions representing the objectives and the constraints are linear. A) Linear programming B) Quadratic programming C) Cubic programming D) Variable programming

4. The ……………….. of a function is mathematically equivalent to the maximization of the negative expression of this function. A) Maximization B) Domain C) Minimization D) Range

5. In ……………. the objective function is used to control the development and evaluation of each feasible solution to the problem. A) Graphical method B) Simplex method C) Linear method D) Quadratic method

6. The right hand side element of each constraint equation is ……………… A) Any real number B) zero C) negative D) non-negative

7. A basic feasible solution that contains less than m + n – 1 non-negative allocations A) Graphical method B) Simplex method C) Linear method D) Quadratic method

8. A feasible solution is said to be …………. if it minimizes the the total transportation cost.

A) negligible B) zero C) optimal D) non-negative

9. ……………….. method is based on the concept of opportunity cost. A) Graphical method B) Simplex method C) VAM Hungarian method D) Hungarian Assignment method

10. Hungarian method of solving an assignment problem requires that the number of columns should be …………….. to the number of rows A) More than B) equal C) less than D) strictly less than

11. …………….. has evolved as a new field with the development of two analytic techniques for planning, scheduling and controlling projects. A) Graphical method B) Simplex method C) VAM Hungarian method D) Project Management

12. ……………….. is used normally for projects involving activities of non-repetitive nature and in which time estimates are uncertain. A) PERT

B) CERT C) DERT D) QERT

13. …………… theory is applicable to situations where the customers arrive at some service station for some service; wait ; and then leave the system after getting the service. A) Queuing theory B) Simplex theory C) VAM Hungarian theory D) Project Management theory

14. The source of customers for a queuing system can be ……………. A) Finite B) Infinite C) A or B D) cannot say

15. Problems in which some variables can take only integer values and some variables can take fractional values are called as …………………… A) Queuing Program B) Mixed Integer Programs C) VAM Hungarian Program D) Integer Program

16. The Gomory’s constraint is ………………….. A) f 10 f 11x 1 f 11x 4 0 B) f 10 f 11x 1 f 11x 4 0 C) f 10 f 11x 1 f 11x 4 0

D) f 10 f 11x 1 f 11x 4 0

17. In Game theory each participant is called …………….. A) Captain B) Gamer C) Player D) Integer

18. If a player decides to use only particular course of action during every play, he is said to use ……….. A) Applied strategy B) Pure strategy C) Strategy D) Mathematical strategy

19. In Game theory each participant is called …………….. A) Captain B) Gamer C) Player D) Integer

20. If a player decides to use only particular course of action during every play, he is said to use …………………… A) Applied strategy B) Pure strategy C) Strategy D) Mathematical strategy

21. ……………… involves determination of objectives, measures of effectiveness and formulation of the problems relative to the objectives. A) Judgment phase B) Applied phase C) Differential phase D) Non-Differential phase.

22. Any inequality in one direction ( or ) may be changed to an inequality in the opposite direction ( or ) by multiplying both sides of the inequality by …………. A) 2 B) 1 C) – 1 D) 0

23. The variable which is …………… in sign( 0, 0) is equivalent to the difference between two non-negative variables. A) Constrained B) Unconstrained C) Constant D) Varying

24. Any non-negative value of (x1, x2) is a ……….. solution of the L.P.P if it satisfies all the constraints. A) Non-feasible B) Feasible C) Standard D) Variable

25. The non-negative variable that has to be added to a constraint inequality of the form to change it to an equation is called a ………………… A) Surplus variable B) Surplus constant C) Slack variable D) Slack constant

26. To each of the constraint equations we add a new variable called a ………………… A) Artificial variable B) Discrete variable C) Indiscrete variable D) Numerical variable

27. If one or more values of the basic variables are also zero valued, then solution of the system is said to ………………….. A) Non degenerate B) Degenerate C) Vanish D) Non-basic

28. An inequality constraint with its left hand side in the absolute form can be changed into two …………… inequalities A) Regular B) Irregular C) Distributive D) Non-distributive

29. ……………… method takes into account not only the least cost cij but also the costs that just exceed cij. A) Simplex method B) Tucker method C) Vogel’s method D) Dickson method

30. The problem becomes ………………….. when two or more cells are vacated simultaneously in the process of transferring units along the closed path. A) Non-degenerate B) Degenerate C) Insolvable D) Optimal

31. ………………. is a problem because people possess varying abilities for performing different jobs and therefore, the costs of performing these jobs by different people are different. A) Duality B) Optimality C) Assignment D) Differentiation

32. …………………… method of solving an Assignment problem requires that the number of columns should be equal to the number of rows. A) Pythagorean B) Archimedean C) Newton D) Hungarian

33. ……………… in the network diagram are identified by numbers. A) Events B) Flows C) Structures D) Blocks

34. A non-critical activity is said to have a …………….. time A) Draw B) Flow C) Float D) Constant

35. The critical path calculations include two phases, the first phase is called the …………….. A) Backward pass B) Forward pass C) Medium pass D) Constant pass

36. The …………….. for activity is the difference between the maximum time available to perform the activity and its duration. A) Small float B) Total float C) Zero float D) Minimal float

37. The expected duration of each activity D A)

a b 4m 5

B) C) D)

a b 4m 6

a b 4m 4

a b 4m 10

38. The variance of each activity is given by ……………………

b a A) 6

3

b a B) 5

3

b a 7

3

b a D) 6

3

C)

39. A critical path is a path of activities, from the start node to the finish node, with ……….. slack time A) 1 B) 2 C) 0 D) –1

40. The average rate at which customers arrive as well as the statistical pattern of arrivals is known as ……………….. A) Service process B) Queue process

C) Arrival process D) Modifying process

Part B (Two mark questions) 41. State true(T) or false(F) The research phase involves i. Formulation of hypothesis and model. ii. Analysis of the available information A) (i) T

(ii) T

B) (i) F

(ii) F

C) (i) T

(ii) F

D) (i) F

(ii) T

42. State true(T) or false(F) The different objective functions in practice are (i) Maximization of cost (ii) Maximization of resource utilization. A) (i) T (ii) T B) (i) F (ii) F C) (i) T (ii) F D) (i) F (ii) T

43) State true(T) or false(F) i. A set X is convex if for any points x1, x2 in X, the line segment joining these points is also in X. ii. A redundant constraint is a constraint which affects the feasible region. A) (i) T

(ii) T

B) (i) F

(ii) F

C) (i) T

(ii) F

D) (i) F

(ii) T

44. State true(T) or false(F) (i) A basic solution of a system of m equations and n variables (m < n) is a solution where atleast n â€“ m variables are zero. (ii) Any feasible solution that optimizes the objective function is called an optimal feasible solution. A) (i) T (ii) T B) (i) F (ii) F C) (i) T (ii) F D) (i) F (ii) T

45. State true(T) or false(F) i. Variables which are assigned value zero initially are called the non-basic variables. ii. A basic solution is said to be non-feasible, if it satisfies all the constraints. A) (i) T

(ii) T

B) (i) F

(ii) F

C) (i) T

(ii) F

D) (i) F

(ii) T

46. State true(T) or false(F) (i) The pivot column is the column with the most positive value in the objective function. (ii) The variables in the both the primal and the dual are negative A) (i) T (ii) T B) (i) F (ii) F C) (i) T (ii) F D) (i) F (ii) T

47. State true(T) or false(F) i. A basic feasible solution that contains more than m + n â€“ 1 non-negative allocations, is called the degenerate basic feasible solution. ii. A transportation problem is said to be balanced if the total supply from all the sources equals the total demand in all the destinations and is called unbalanced otherwise. A) (i) T

(ii) T

B) (i) F

(ii) F

C) (i) T

(ii) F

D) (i) F

(ii) T

48. State true(T) or false(F) (i) If the number of occupied cells is less than m + n â€“ 1, then the solution is called a degenerate solution. (ii) An independent cell is the one from which a closed loop cannot be traced. A) (i) T (ii) T B) (i) F (ii) F C) (i) T (ii) F D) (i) F (ii) T

49. State true(T) or false(F) i. The solution to an assignment problem can be obtained by complete enumeration and evaluation of all possible assignments. ii. Multiple zeros in all columns and rows are indicative of multiple optimal solutions. A) (i) T

(ii) T

B) (i) F

(ii) F

C) (i) T

(ii) F

D) (i) F

(ii) T

50. State true(T) or false(F) (i) An assignment problem can be obtained by complete enumeration and evaluation of all possible assignments. (ii) For every prohibited assignment, the given cost element is replaced by M, which is a very small value. A) (i) T (ii) T B) (i) F (ii) F C) (i) T (ii) F D) (i) F (ii) T

51. State true(T) or false(F) i. CPM is used for projects involving activities of repetitive nature. ii. Project control refers to revaluating actual progress against the plan. A) (i) T

(ii) T

B) (i) F

(ii) F

C) (i) T

(ii) F

D)(i) F

(ii) T

52. State true(T) or false(F) (i) An event represents a point in time that signifies the completion of some activities and the beginning of new ones. (ii) Activities of the network represent project operations or task that has already been conducted. A) (i) T (ii) T B) (i) F (ii) F C) (i) T (ii) F D) (i) F (ii) T

53. State true(T) or false(F) The different bases on which the arrivals from the input population may be classified are i. According to availability ii. According to numbers A) (i) T

(ii) T

B) (i) F

(ii) F

C) (i) T

(ii) F

D) (i) F

(ii) T

54. State true(T) or false(F) (i) Service rate describes the number of customers serviced during a particular time period. (ii) The service time indicates the amount of time needed to service a customer. A) (i) T (ii) T B) (i) F (ii) F C) (i) T (ii) F D) (i) F (ii) T

55. State true(T) or false(F) i. The Branching is the simple operation that divides a program into two subproblems, such that the solution of the original problem can be found from the solutions of the main problems. ii. The bounding operation is a function that returns a bound on the optimal solution of the current subproblem. A) (i) T

(ii) T

B) (i) F

(ii) F

C) (i) T

(ii) F

D) (i) F

(ii) T

56. State true(T) or false(F) Some of the main ideas of Branch and Bound technique is

(i) If the relaxed problem is infeasible-backtrack. (ii) If the solution is integral-terminate. A) (i) T (ii) T B) (i) F (ii) F C) (i) T (ii) F D) (i) F (ii) T

57. State true(T) or false(F) i. A game with two players, where a gain of one player equals the loss to the other is known as a two-person zero-sum game. ii. A payoff is a rule strictly followed when playing a game. A) (i) T

(ii) T

B) (i) F

(ii) F

C) (i) T

(ii) F

D) (i) F

(ii) T

58. State true(T) or false(F) Characteristic of a Two-person-zero-sum game is (i) Only two players participate (ii) Each specific strategy results in a payoff. A) (i) T (ii) T B) (i) F (ii) F C) (i) T (ii) F D) (i) F (ii) T

59. State true(T) or false(F) i. Standard error is volatile ii. A simulation model involves several variables. A) (i) T

(ii) T

B) (i) F

(ii) F

C) (i) T

(ii) F

D) (i) F

(ii) T

60. State true(T) or false(F) The following are the phases of the simulation process (i) Construction of an appropriate model (ii) Experiments with the model constructed A) (i) T (ii) T B) (i) F (ii) F C) (i) T (ii) F D) (i) F (ii) T

Part C (Four mark questions) 61. The OR approach to problem solving consists of the following steps 1. Definition of the problem 2. Formation of a mathematical model. 3. Validation of the solution 4. Solution of the mathematical model 5. Implementation of the solution The correct hierarchy is A) 1, 2, 3, 4, 5 B) 1, 2, 5, 4, 3 C) 1, 2, 4, 3, 5 D) 2, 1, 3, 4, 5

62. The solution of the L.P.P. is Maximize

Z 40x 1 60x 2 2x 1 x 2 70

x 1 x 2 40

x 1 3x 2 90

x 1 0, x 2 0 A) bounded B) recursive C) unbounded D) infinite

63. Using the Simplex method the solution of the L.P.P. Maximize Z 5x 1 3x 2 subject to the constraints

x1 x 2 2 5x 1 2x 2 10

3x 1 8x 2 12

x 1, x 2 0 A) Max Z = 10 B) Max Z = 20 C) Max Z = 15 D) Max Z = 11

64. The solution for the transportation problem given below by North West Corner rule is

To

From

Demand

1

2

3

4

Supply

A 7

3

8

6

60

B 4

2

5

10 100

C 2

6

5

1

20 50 50

40

80 200

A) Max Z = 10 B) Max Z = 20 C) Max Z = 15 D) Max Z = 11

65. The optimal solution to the assignment problem given below by HAM is Worker

Job A

B

C

D

1

45

40

51

67

2

57

42

63

55

3

49

52

48

64

4

41

45

60

55

A) 190 min B) 195 min C) 150 min D) 184 min

66. State whether true(T) or false(F) (i) In a project network, a sequence of activities may form a loop. (ii) A critical activity must have its total and free floats equal to zero. (iii) A non-critical activity cannot have zero total float. (iv) A network may include more than one critical path. A) (i) T (ii) T (iii) F (iv) T B) (i) F (ii) T (iii) F (iv) T C) (i) F (ii) T (iii) T (iv) F D) (i) T (ii) T (iii) T (iv) T

67. Ships arrive to a port at a rate of one in every 3 hours, with a negative exponential distribution of inter arrival times. The time a ship occupies a berth for unloading and loading has a negative exponential distribution with an average of 12 hours. If the average delay of ships waiting for berths is to be kept below 6 hours, how many berths should there be at the port. A) 7 B) 6 C) 8 D) 9

68. Using Branch and Bound technique solve the I.P.P. Maximize Z 7x 1 9x 2 Subject to the constraints

x 1 3x 2 6 7x 1 x 2 35

0 x 1, x 2 7

x 1, x 2 are integers A) 65 B) 55 C) 45 D) 75

69. Reducing the following game by dominance, the game value is

Player B

Player A

A)

4 3

B)

6 3

C)

7 3

D)

8 3

I

II

III

IV

I

3

2

4

0

II

3

4

2

4

III

4

2

4

0

IV

0

4

0

8

70. At Indian oil petrol pump, customers arrive according to a Poisson process with an average time of 5 minute between arrivals. The service time is exponentially distributed with mean time = 2 min. On the basis of this information, find out the average waiting time of a car before receiving petrol? A) 2 min B) 1.8 min C) 1.33 min D) 1 min

71. Using Penalty Cost method solve the problem Maximize Z = 2x1 + 3x2 Subject to x1 + 2x2 ď‚Ł 2

6x1 + 4x2 24 x1, x2 0 A) Z = 5 B) Z = 9 C) Z = 4 D) No solution

72. Solve the L.P.P Maximize Z = 12x1 + 3x2 + x3 Subject to 10x1 + 2x2 + x3 100 7x1 + 3x2 + 2x3 77 2x1 + 4x2 + x3 80 x1, x2, x3 0 The optimum value of the objective function is A) Z

981 8

B) Z

981 11

C) Z

981 7

D) Z

900 8

73. Solve the following transportation problem Destination

Source

Requirement

A

B

C

D

I

21

16 25

13

11

II

17

18 14

23

13

III

32

27 18

41

19

6

10 12

15

43

A) Rs 596 B) Rs 696 C) Rs 796 D) Rs 496

74. A solicitorâ€™s firm employs typists on hourly piece-rate basis for their daily work. There are five typists and their charges and speed are different. According to an earlier understanding, only one job is given to one typist and the typist is paid for a full hour even when he works for a fraction of an hour. Find the total cost allocation for the following data:

Typist

Rate/hour(Rs) Number of Page

Job

Typist/hour

A) 499 B) 599 C) 399 D) 799

No. of Pages

A

5

12

P

199

B

6

14

Q

175

C

3

8

R

145

D

4

10

S

298

E

4

11

T

178

75. State true(T) or False(F) The general structure of a Queuing system consists of the following (i) Arrival process (ii) Service facility (iii) profit discipline A) (i) T (ii) T (iii) T B) (i) T (ii) T (iii) F C) (i) F (ii) F (iii) T D) (i) F (ii) F (iii) F

Part - A Q. No.

Ans. Key

Part - B

Q. No.

Ans. Key

Q. No.

Part - C

Ans. Key

Q. No.

Ans. Key

1

A

21

B

41

A

61

C

2

C

22

C

42

D

62

C

3

A

23

B

43

C

63

A

4

C

24

B

44

A

64

A

5

B

25

C

45

C

65

D

6

D

26

A

46

B

66

C

7

B

27

B

47

D

67

B

8

C

28

A

48

A

68

B

9

D

29

C

49

C

69

D

10

B

30

B

50

C

70

C

11

D

31

C

51

A

71

D

12

A

32

D

52

C

72

A

13

A

33

A

53

D

73

C

14

C

34

C

54

A

74

C

15

B

35

B

55

C

75

B

16

D

36

C

56

A

17

C

37

B

57

C

18

B

38

A

58

A

19

C

39

C

59

D

20

B

40

C

60

A