**T.Y B.COM**

**SEMESTER - 5**

**MID SEMESTER EXAMINATION**

**OPERATIONS RESEARCH**

**(OR)**

**100 - MCQS**

**1. _________ are expressed is the form of inequities or equations**

**a) Constraints**

b) Objective Functions

c) Both A and B

d) None of the above

**2. The objective functions and constraints are linear relationship between ________**

**a) Variables**

b) Constraints

c) Functions

d) All of the above

**3. Assignment problem helps to find a maximum weight identical in nature in a weighted __________**

a) Tripartite graph

**b) Bipartite graph**

c) Partite 8raph

d) None of the above

**4. All the parameters in the linear programming model are assumed to be _______**

a) Variables

**b) Constraints**

c) Functions

d) None of the above

**5. The solution need not be in ________ numbers**

a) Prime Number

**b) Whole Number**

c) Complex Number

d) None of the above

**6. Graphic method can be applied to solve a LPP when there are only ________ variable**

a) One

b) More than One

**c) Two**

d) Three

**7. If the feasible region of a LPP is empty, the solution is _______**

**a) Infeasible**

b) Unbounded

c) Alternative

d) None of the above

**8. The variables whose coefficient vectors are unit vectors are called _________**

a) Unit Variables

**b) Basic Variables**

c) Non basic Variables

d) None of the above

**9. Any column or raw of a simplex table is called a ________**

**a) Vector**

b) Key column

c) Key Raw

d) None of the above

**10. If there are 'm' original variables and 'n' introduced variables, then there will be ______ columns in the simplex table**

a) M + n

b) M - n

c) 3 + m + n

d) M + n - 1

**11. A minimization problem can be converted into a maximization problem by changing the sign of coefficients in the _______**

a) constraints

**b) Objective Functions**

c) Both A and B

d) None of the above

**12. If in a LPP , the solution of a variable can be made infinity large without violating the constraints, the solution is _________**

a) Infeasible

**b) Unbounded**

c) Alternative

d) None of the above

**13. In maximization cases, ___________ are assigned to the artificial variables as their coefficients in the objective function**

**a) +m**

b) -m

c) 0

d) None of the above

**14. In simplex method, we add __________ variables in the case of '='**

a) Slack Variable

b) Surplus Variable

**c) Artificial Variable**

d) None of the above

**15. In simplex method, if there is tie between a decision variable and a slack (or surplus) variable, __________ should be selected**

a) Slack variable

b) Surplus variable

**c) Decision variable**

d) None of the above

**16. A BFS of a LPP is said to be ________ if at least one of the basic variable is zero**

**a) Degenerate**

b) Non-degenerate

c) Infeasible

d) Unbounded

**17. In LPP, degeneracy occurs in _________ stages**

a) One

**b) Two**

c) Three

d) Four

**18. Every LPP is associated with another LPP is called ________**

a) Primal

**b) Dual**

c) Non-linear programming

d) None of the above

**19. As for maximization in assignment problem, the objective is to maximize the _________**

**a) Profit**

b) optimization

c) cost

d) None of the above

**20. If there are more than one optimum solution for the decision variable the solution is _______**

a) Infeasible

b) Unbounded

**c) Alternative**

d) None of the above

**21. Dual of the dual is _________**

**a) Primal**

b) Dual

c) Alternative

d) None of the above

**22. Operations Research approach is**

a) Multi-disciplinary

b) Scientific

**c) Initiative**

d) All of the above

**23. For analyzing the problem, decision - makers should normally study**

**a) Its qualitative aspects**

b) Its quantitative aspects

c) Both A and B

d) Neither A and B

**24. Decision variables are**

a) Controllable

b) Uncontrollable

c) Parameters

**d) None of the above**

**25. The issue of decision models**

a) Is possible when the variable's value is

b) Reduces the scope of judgment and intuition known with certainty in decision making

c) Requires the knowledge of computer software use

**d) None of the above**

**26. _________ is one of the fundamental combinatorial optimization problems.**

**a) Assignment problem**

b) Transportation problem

c) Optimization Problem

d) None of the above

**27. An optimization model**

a) Mathematically provides the best decision

b) Provides decision within its limited context

c) Helps in evaluating various alternatives constantly

**d) All of the above**

**28. The quantitative approach to decision analysis is a**

a) Logical approach

b) Rational approach

**c) Scientific approach**

d) All of the above

**29. Operations Research approach is typically based on the use of**

a) Physical model

**b) Mathematical model**

c) lconic model

d) Descriptive model

**30. In a manufacturing process, who takes the decisions as to what quantities and which process or processes are to be used so that the cost is minimum and profit is maximum?**

a) Supervisor

b) Manufacturer

c) Producer

**d) Production manager**

**31. Linear programming has been successfully applied in ________**

a) Agricultural

b) Industrial applications

**c) Both A and B**

d) Manufacturing

**32. The term linearity implies _________ among the relevant variables:**

a) Straight line

b) Industrial applications

c) Linear lines

**d) Both A and B**

**33. Process refers to the combination of _________ inputs to produce a particular output.**

**a) one or more**

b) two or more

c) one

d) None of the above

**34. What has always been very important in the business and industrial world, particularly with regard to problems concerning productions of commodities?**

a) Linear Programming

b) Production

**c) Decision - making**

d) None of the above

**35. What are the main questions before a production manager?**

a) Which commodity/ commodities to produce

b) In what quantities

c) By which process or processes

**d) All of the above**

**36. Who pointed out that the businessman always studies his production function and his input prices and substitutes one input for another till his costs become the minimum possible?**

a) Alan Marshall

b) Alfred Marsh

**c) Alfred Marshall**

d) None of the above

**37. Who invented a method of formal calculations often termed as ?**

a) A.V. Kantorovich

b) LV. Kantorovich

c) T.S. Kantorovich

**d) Alfred Marshall**

**38. Who developed Linear Programming for the purpose of scheduling the complicated procurement activities of the United States Air Force?**

**a) George B. Dantzig**

b) James B. Dantzig

c) George B. Dante

d) George V. Dantzig

**39. This method of formal calculations often termed as Linear Programming was developed later in which year?**

**a) 1947**

b) 1988

c) 1957

d) 1944

**40. What is being considered as one of the most versatile management tools?**

a) Electronic Computers

**b) Linear Programming**

c) Computer Programming

d) None of the above

**41. LP is a major innovation since ________ in the field of business decision - making, particularly under conditions of certainty.**

a) Industrial Revolution

b) World War I

**c) World War II**

d) French Revolution

**42. The world "Linear" means that the relationships are represented by _______**

a) Diagonal lines

b) Curved lines

**c) Straight lines**

d) Slanting lines

**43. The world 'programming' means taking decisions ________**

**a) Systematically**

b) Rapidly

c) Slowly

d) Instantly

**44. Who originally called it 'Programming of interdependent activities in a linear structure' but later shortened it to 'Linear Programming' ?**

**a) Dantzig**

b) Kantorovich

c) Marshall

d) None of the above

**45. LP can be applied in farm management problems is relates to the allocation of resources such as _________ in such a way that is maximizes net revenue**

a) Acreage

b) Labor

c) Water supply or working capital

**d) All of the above**

**46. LP model is based on the assumptions of _________**

a) Proportionality

b) Additivity

c) Certainty

**d) All of the above**

**47. __________ assumption means the prior knowledge of all the coefficients in the objective function, the coefficients of the constraints and the resource values.**

a) Proportionality

**b) Certainty**

c) Finite choices

d) Continuity

**48. Simple linear programming problem with _________ variables can be easily solved by the graphical method.**

a) One decision

b) Four decisions

c) Three decisions

**d) Two decisions**

**49. Any solution to a LPP which satisfies the non- negativity restrictions of the LPP is called its ________**

a) Unbounded solution

b) Optimal solution

**c) Feasible solution**

d) Both A and B

**50. Any feasible solution which optimizes (minimizes or maximizes) the objective function of the LPP is called its _______**

**a) Optimal solution**

b) Non-basic variables

c) Solution

d) Basic feasible solution

**51. A non-degenerate basic feasible solution is the basic feasible solution which has exactly m positive Xi (i=1,2,..,m), i.e., none of the basic variable is ______**

a) Infinity

b) One

**c) Zero**

d) X

**52. What is also defined as the non-negative variables which are added in the LHS of the constraint to convert the inequality '_ ' into an equation?**

**a) Slack variables**

b) Simplex algorithm

c) Key element

d) None of the above

**53. Which method is an iterative procedure for solving LPP in a finite number of steps?**

a) Simplex algorithm

b) Slack variable

c) M method

**d) Simplex method**

**54. In simplex algorithm , which method is used to deal with the situation where an infeasible starting basic solution is given?**

a) Slack variable

b) Simplex method

**c) M-method**

d) None of the above

**55. How many methods are there to solve LPP?**

a) Three

**d) Two**

c) Four

d) None of the above

**56. ________ is another method to solve a given LPP involving some artificial variable ?**

a) Big M method

b) Method of penalties

**c) Two-phase simplex method**

d) None of the above

**57. Which variables are fictitious and cannot have any physical meaning ?**

a) Optimal variable

b) Decision variable

**c) Artificial variable**

d) None of the above

**58. An objective function which states the determinants of the quantity to be either maximized or minimized is called __________**

a) Feasible function

b) Optimal function

**c) Criterion function**

d) None of the above

**59. An assumption that implies that finite numbers of choices are available to a decision - maker and the decision variables do not assume negative values is known as __________**

a) Certainty

b) Continuity

**c) Finite choices**

d) None of the above

**60. A set of values X1, X2,..Xn which satisfies the constraints of the LPP is called _______**

**a) Solution**

b) Variable

C) Linearity

d) None of the above

**61. A basic solution which also satisfies the condition in which all basic variables are non -negative is called ________**

**a) Basic feasible solution**

b) Feasible solution

c) Optimal solution

d) None of the above

**62. All the constraints are expressed as equations and the right hand side of each constraint and all variables are non-negative is called _______**

a) Canonical variable

**b) Canonical form**

c) Canonical solution

d) Both A and B

**63. An objective function is maximized when it is a _________ function**

a) Passive

**b) Profit**

c) Cost

d) None of the above

**64. LPP is exactly used in solving what kind of resource allocation problems?**

a) Production planning and scheduling

b) Transportation

c) Sales and advertising

**d) All of the above**

**65. Currently, LPP is used in solving a wide range of practical _________**

**a) Business problems**

b) Agricultural problems

c) Manufacturing problems

d) None of the above

**66. __________ refers to the combination of one or more inputs to produce a particular output.**

a) Solution

b) variable

**c) Process**

d) None of the above

**67. An optimum solution is considered the _________ among feasible solutions.**

a) Worst

**b) Best**

c) Ineffective

d) None of the above

**68. Please state which statement is true.**

**(i) All linear programming problems may not have unique solutions**

**(ii) The artificial variable technique is not a device that does not get the starting basic feasible solution.**

a) Both (i) and (ii)

b) (ii) only

**c) (i) only**

d) Both are incorrect

**69. Please state which statement is incorrect.**

**(i)Linear programming was first formulated by an English economist L.V. Kantorovich**

**(ii) LP is generally used in solving maximization or minimization problems subject to certain assumptions.**

a) (ii) only

**b) (i) only**

c) Both (i) and( ii)

d) Both are correct

**70. _____________ which is a subclass of a linear programming problem (LPP)**

a) Programming problem

**b) Transportation problem**

c) Computer problem

d) Both are incorrect

**71. The solution of any transportation problem is obtained in how many stages?**

a) Five

b) Four

c) Three

**d) Two**

**72. An optimal solution is the _______ Stage of a solution obtained by improving the initial solution**

a) Third

b) First

**c) Second**

d) Final

**73. MODI method is used to obtain _______**

a) Optimal solutions

b) Optimality test

**c) Both A and B**

d) Optimization

**74. For solving an assignment problem, which method is used?**

**a) Hungarian**

b) American

c) German

d) Both are incorrect

**75. To make an unbalanced assignment problem balanced, what are added with all entries as zeroes?**

a) Dummy rows

b) Dummy columns

**c) Both A and B**

d) Dummy entries

**76. Any set of non-negative allocations (Xij>0) which satisfies the raw and column sum (rim requirement ) is called a _____________**

a) Linear programming

b) Basic feasible solution

**c) Feasible solution**

d) None of the above

**77. A feasible solution is called a basic feasible solution if the number of non-negative allocations is equal to __________**

a) m-n+1

b) m-n-l

**c) m+n-1**

d) None of the above

**78. Any feasible solution to a transportation problem containing m origins and n destinations is said to be ____________**

a) Independent

b) Degenerate

**c) Non-degenerate**

d) Both A and B

**79. A path formed by allowing horizontal and vertical lines and the entire corner cells of which are**

**Occupied is called a __________**

a) Occupied path

b) Open path

**c) Closed path**

d) None of the above

**80. Transportation algorithm can be used for minimizing the transportation cost of _________ from O origins and D destinations**

**a) Goods**

b) Products

c) Items

d) None of the above

**81. If demand is lesser than supply then dummy demand node is added to make it a __________**

a) Simple problem

**b) Balanced problem**

c)Transportation problem

d) None of the above

**82. Basic cells indicate positive values and non- basic cells have _________ value for flow**

a) Negative

b) Positive

c) One

**d) zero**

**83. According to transportation problem number of basic cells will be exactly ___________**

a) m+n-0

b) n+m-1

**c) m+n-1**

d) None of the above

**84. Before starting to solve the problem, it should be balanced. If not then make it balanced by _____________ column incase demand is less than supply or by adding _________**

**raw incase supply is less**

**than the demand**

a) 0,D

b) m,n

c) Horizontal, Vertical

**d) Unshipped supply, Shortage**

**85. In which phase is optimization done and how does that phase also checks for optimality conditions?**

a) Phase II

b) Phase I

**c) Phase II**

d) None of the above

**86. Optimality conditions are expressed as ________ incase all non-basic cells?**

a) Negligent costs

b) Advanced costs

**c) Reduced costs**

d) None of the above

**87. A __________ has rows/ column having non- basic cells for holding compensating (+) or (-) sign.**

**a) Cycle**

b) Dead- end

c) Back track

d) None of the above

**88. After determining every basic cell with in this cycle, adjustment is obtained as minimum value in basic cells. this is known as ________**

a) Adjustment amount

b) aa

**c) Both A and B**

d) Alternatives

**89. Optimal solution is a feasible solution (not necessarily basic ) which minimizes the _________**

a) Time taken

b) Partial cost

**c) Total cost**

d) None of the above

**90. State which of the two statements is correct**

**(i) the cells in the transportation table can be classified in to occupied cells and unoccupied cells**

**(ii) optimal solution is a feasible solution (not necessarily basic) which maximizes the total cost**

a) both (i) and (ii) are correct

b) Two only

**c) One only**

d) Both (i) and (ii) are incorrect

**91. The allocated cells in the transportation table are called ______**

a) Occupied cells

b) Empty cells

**c) Both A and B**

d) Unoccupied cells

**92. VAM stands for _______**

a) Vogel's Approximation Method

b) Vogel's Approximate Method

c) Vangelis Approximation Method

**d) Vogel's Approximation Method**

**93. Once the initial basic feasible solution has been computed, what is the next step in the problem**

a) VAM

b) Modified distribution method

**c) Optimality test**

d) None of the above

**94. One can find the initial basic feasible solution by using ?**

**a) VAM**

b) MODI

c) Optimality test

d) None of the above

**95. What do we apply in order to determine the optimum solution ?**

a) LPP

b) VAM

**c) MODI Method**

d) None of the above

**96. In a TP, if the number of non-negative independent allocation is ________ than m+n-1.**

a) Equivalent

b) Greater

**c) Less**

d) None of the above

**97. A given TP is said to be unbalanced, if the total supply is not equal to the total ________**

a) Optimization

**b) Demand**

c) Cost

d) None of the above

**98. If the total supply is less than the total demand, a dummy source (row) is included in the cost matrix with ________**

a) Dummy Demand

b) Dummy Supply

**c) Zero Cost**

d) Both A and B

**99. To find the optimal solution, we apply _________**

a) LPP

b) VAM

**c) MODI Method**

d) Rim

**100. For maximization in TP , the objective is to maximize the total ________**

a) Solution

b) Profit Matrix

**c) Profit**

d) None of the above

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