FR2
1.
2.
3.
4.
5.
6.
7.
8.
Operation research approach is
(a) Multi- disciplinary
(b) Scientific
(c) Intuitive
(d) All of the above
Operation research analysis do not –
(a) Predict future operations
(b) Build more than one model
(c) Collect relevant data
(d) All of the above
Decision variables are –
(a) Controllable
(b) Uncontrollable
(c) Parameters
(d) None of the above
A model is –
(a) An essence of reality
(b) An approxionation
(c) An idealization
(d) All of the above
Every mathematical model
(a) Must be deterministic
(b) Requires computers aid for its
solution
(c) Represents data in numerical form
(d) All of the above
A physical model is example of –
(a) Iconic model
(b) Analogue model
(c) A verbal model
(d) None of the above
Linear programming is a tool of –
(a) Operation research
(b) Mathematical research
(c) Statistical research
(d) None of the above
A L.P.P.
Max z = 2x1 + 2x2
s.t
x1 + 2x2 ≤ 10
x1 – x2 ≤ 6
x1 – x2 ≤ 2
x1 - 2x2 ≤ 1
x1 x2 7,0 hences 07
(a) x1=4,x2=2 z max = 100
(b) x1 = 4, x2 = 2, z max = 10
(c) x1 = 4 x2 =4, z max = 10
(d) x1=4,x2=5 z max = 200
XIX
9.
10.
11.
12.
13.
14.
15.
Mathematical model of LP problem is
important because –
(a) it helps is converting the verbal
description and numerical data into
mathematical expression
(b) Decision – maker prefers to works
with formal models
(c) It captures the relevant relationships
among decision factors
(d) It enables the use of algebraic
technique
Linear programming is a –
(a) Constrained optimization technique
(b) Technique for economic allocation
of limited resources
(c) Mathematical technique
(d) All of the above
A constraint in an LP model restricts –
(a) Value of objective function
(b) Value of decision variable
(c) Use of the available resource
(d) All of the above
The distinguishing feature an LP model
is –
(a) Relationship among all variables is
linear
(b) It has single objective function and
constraints
(c) Value of decision variable is nonnegation
(d) All of the above
Constraints is an LP model represents
(a) Limitations
(b) Requirements
(c) Balancing limitations and requirements
(d) All of the above
Non-negativity condition is an important
component of LP model represents.
(a) Variables value should remain
under the control of decision model
(b) Value of variables make sense and
correspond to real world problems
(c) Variables are interrelated in terms
of limited resources
(d) None of the above
Before formulating a formal LP model, it
is better to –
(a) Empress each constraints in words
(b) Empress the objective function in
words
(c) Decision variables are identified
verbally
(d) All of the above
(1)
FR2
16. Each constraints is an LP model is
impressed as an –
(a) Inequality with z sign
(b) Inequality with ≤ sign
(c) Equation with = sing
(d) None of the above
17. Minimization of objective function in LP
model means –
(a) Value accurse at allowable set of
decisions
(b) Highest value is chosen among
allowable decision
(c) Both (a) and (b)
(d) None of the above
18. Which of the following is not a
characterization of LP model?
(a) Alternation courses of action
(b) An
objective
function
of
maximization type
(c) Limited amount of resources
(d) Non-negativity condition on the
value of decision variables
19. The graphical method of LP problem
uses
(a) Objective function equation
(b) Constraint equations
(c) Linear equations
(d) All of the above
20. A feasible solution to an LP problem
(a) Must satisfy all of the constraints,
simultaneously
(b) Need not satisfy all of the
constraints, only some of them
(c) Must be a corner point of the
feasible region
(d) Must optimize the value of the
objective function
21. Which of the following statements is
true with respect to the optimal solution
of an LP problem
(a) Every LP problem has an optimal
solution
(b) Optimal solution of an LP problem
always occurs at an extreme point
(c) At optimal solution all resources are
used completely
(d) If an optimal solution exists, there
will always be at least one at a
corner
XIX
22. An ISO – profit line represents –
(a) An infinite number of solutions all of
which yield the same profit
(b) An infinite number of solutions all of
which yield the same cost
(c) An infinite number of optimal solution
(d) A boundary of the feasible region
23. If an ISO - profit line yielding the
optimal solution coincides with a
constant line, then
(a) The solution is unbounded
(b) The solution is infeasible
(c) The constraint which coincides is
redundant
(d) None of the above
24. While plotting constraints on a graph
paper, terminal point on both the axes
are connected by straight line because
(a) The resources are limited in supply
(b) The objectives function is a linear
function
(c) The constraints are linear equations
or inequalities
(d) All of the above
25. A constraint in an LP model becomes
redundant because
(a) Two-ISO-profit line may be parallel
to each other
(b) The solution is unbounded
(c) This constraint is not satisfied by
the solution values
(d) None of the above
26. If two constraints do not intersect in the
positive quadrant of the graph, then
(a) The problem is infeasible
(b) The solution is unbounded
(c) One of the constraints is redundant
(d) None of the above
27. Constraints is LP problem are called
active if they
(a) Represent optimal solution
(b) At optimality do not consume all the
available resources
(c) Both (a) the (b)
(d) None of the above
28. The solution space (region) of an LP
problem is unbounded due to –
(a) An incorrect formulation of the LP
model
(b) Objective function is unbounded
(c) Both (a) the (b)
(d) None of the above
(2)
FR2
29. The role of artificial variables in the
simplex method is –
(a) To aid in finding an initial solution
(b) To find optimal dual prices in the
final simplex table
(c) To start phases of simplex method
(d) All of the above
30. For a maximization problem, the
objective function coefficient for an
artificial variable is –
(a) + M
(b) – M
(c) Zero
(d) None of the above
31. If a negative values appears in the
solution values (XB) column of the
simplex table, then
(a) The solution is optimal
(b) The solution is infeasible
(c) The solution is unbounded
(d) All of the above
32. At every iteration of simplex method, for
minimization problem, a variable in the
current basis is replaced with another
variable that has –
(a) A positive cj – zj value
(b) A negative cj – zj value
(c) cj – zj = 0
(d) None of the above
33. In the optimal simplex table, cj – zj = 0
value indicates
(a) Unbounded solution
(b) Cycling
(c) Alternative solution
(d) Infeasible solution
34. For maximization LP model, the simplex
method is terminated when all values –
(a) cj – zj ≤ 0
(b) cj – zj ≥ 0
(c) cj – zj = 0
(d) zj ≤ 0
35. A variable which does not appear in the
basic variable (B) column of simplex table is
(a) Never equal to zero
(b) Always equal to zero
(c) Called a basic variable
(d) None of the above
36. If for a given solution, a slack variable
is equal to zero, then
(a) The solution is optimal
(b) The solution is infeasible
(c) The entire amount of resource with the
constraint in which the slack variable
appears has been consumed
(d) All of the above
XIX
37. If an optimal solution is degenerate,
then –
(a) There are alternative optimal
solutions
(b) The solution is infeasible
(c) The solution is of no use to the
decision – maker
(d) None of the above
38. To formulate a problem for solution by
the simplex method, we must add
artificial variable to –
(a) Only equality constraints
(b) Only ‘greater than’ constraints
(c) Both (a) the (b)
(d) None of the above
39. The dual of the primal maximization LP
problem having m constraints and n
non-negative variables should
(a) Have n constraints and m nonnegative variables
(b) Be a minimization LP problem
(c) Both (a) the (b)
(d) None of the above
40. For any primal problem and its dual
(a) Optimal value of objective functions
is same
(b) Primal will have an optimal solution
if and only if dual does too
(c) Both primal and dual cannot be
infeasible
(d) All of the above
41. The right hand side constant of a
constraint in a primal problem appears
in the corresponding dual as
(a) A coefficient in the objective
functions
(b) A right hand side constant of a
constraint
(c) An input-out coefficient
(d) None of the above
42. Dual LP problem approach attempts to
optimize resources allocation by
ensuring that
(a) Marginal opportunity cost of a
resource equals its margin return
(b) Marginal opportunity cost of a
resource is less than its marginal
return
(c) Both (a) the (b)
(d) None of the above
(3)
FR2
43. Shadow price indicates how much one
unit change in the resource value will
change the
(a) Optimality range of an objective
function
(b) Optimal value of the objective
function
(c) Value of the basic variable in the
optimal solution
(d) None of the above
44. Principle of complementary slackness
states that –
(a) Primal slack * dual main = 0
(b) Primal main * dual surplus = 0
(c) Both (a) the (b)
(d) None of the above
45. If dual has an unbounded solution
primal has –
(a) No feasible solution
(b) Unbounded solution
(c) Feasible solution
(d) None of the above
46. If at the optimality a primal constraint
has positive value of slack variable,
then
(a) Dual variable corresponding to that
constraint has zero value
(b) Corresponding resource is not
completely used up
(c) Corresponding resource have zero
opportunity cost
(d) Both (a) the (c) but not (a)
47. The shadow price is –
(a) The price that is paid for purchase
of resource
(b) The saving by eliminating one of the
emcees quantities of resources
(c) The increase in the objective
function value by providing are
additional unit of resources
(d) None of the above
48. The value of dual variable –
(a) Represent marginal profit of each
additional unit of resources
(b) Can be obtained by examining the
zj row of primal optimal simplex
table
(c) Can be obtained by examining cj –
zj row of primal optimal simplex
table
(d) All of the above
XIX
49. The initial solution of a transportation
problem can be obtained by applying
any known method. However, the only
condition is that
(a) The solution be optimal
(b) The rim conditions are satisfied
(c) The solution not be degenerate
(d) All of the above
50. The dummy source or destination in a
transportation problem is added to
(a) Satisfy rim conditions
(b) Prevent solution from becoming
degenerate
(c) Ensure that total cost does not
exceed a limit
(d) None of the above
51. The occurrence of degeneracy while
solving a transportation problem mean
that
(a) Total supply equals total demand
(b) The solution so obtained is not
feasible
(c) The few allocations become
negative
(d) None of the above
52. An alternative optimal solution to a
minimization transportation problem
exists whenever opportunity cost
corresponding to unused route of
transportation is –
(a) Positive and grater than zero
(b) Positive with at least one equal to zero
(c) Negative with at least on equal to
zero
(d) None of the above
53. One disadvantage of using North –
west corner rule to final initial solution
to the transportation problem is that
(a) It is complicated to use
(b) It does not take into account cost of
transportation
(c) It leads to a degenerate initial solution
(d) All of the above
54. The solution to a transportation
problem with m –row (supplies) and n –
columns(destination) is feasible if
number of positive allocations are –
(a) m + n
(b) m * n
(c) m + n – 1
(d) m + n + 1
(4)
FR2
55. The calculation of opportunity cost in
the MODI method is analogous to a –
(a) cj – zj value for non-basic variable
columns in the simplex method
(b) value of a variable in XB -column of
the simplex method
(c) variable in the B column in the
simplex method
(d) None of the above
56. An unoccupied cell in the transportation
method is analogous to a –
(a) cj – zj value in the simplex method
(b) Variable in the B column in the
simplex method
(c) Variable not in the B column in the
simplex method
(d) Value in the XB column in the
simplex method
57. If we were to use opportunity cost value
for an unused cell to test optimality, it
should be –
(a) Equal to zero
(b) Most negative number
(c) Most positive number
(d) Any value
58. During an iteration while from one
solution to the next, degeneracy may
occur when
(a) The closed path indicates a
diagonal move
(b) Two or more occupied cells are on
the closed path but neither of them
represents a corner of the path
(c) Two or more occupied cells on the
closed path with minus sign are tied
for lowest circled value
(d) All of the above
59. Maximization assignment problem is
transformed
into
a
minimization
problem by –
(a) Adding each entry in a column from
the maximum value in that column
(b) Subtracting each entry in a column from
the maximum value in that column
(c) Subtracting each entry in the table from
the maximum value in that table
(d) All of the above
XIX
60. If there were n workers and n fobs
there would be –
(a) n! solutions
(b) (n – 1)! Solutions
(c) (n!)” solutions
(d) n solutions
61. an assignment problem can be solved by
(a) Simplex method
(b) Transportation method
(c) Both (a) the (b)
(d) None of the above
62. For a salesman who has to visit n
cities, following are the wages of his
tour plan
(a) n!
(b) (n + 1)!
(c) (n – 1)!
(d) n
63. The assignment problem
(a) Requires that only one activity be
assigned to each resource
(b) Is a special case of transportation
problem
(c) Can be used to maximize resources
(d) All of the above
64. An assignment problem is considered
as a particular case of a transportation
problem because
(a) The number of row equals columns
(b) All xij = 0 or 1
(c) All rim conditions are 1
(d) All of the above
65. An optimal assignment requires that the
maximum number of linear which can
be drawn through squares with zero
opportunity cost be equal to the number
of
(a) Rows or columns
(b) Rows and columns
(c) Rows + columns – 1
(d) None of the above
66. While solving an assignment problem,
an activity is assigned to a resource
through a squale with zero opportunity
cost because the objective is to
(a) Minimize total cost of assignment
(b) Reduce the cost of assignment to
zero
(c) Reduce the cost of that particular
assignment to zero
(d) All of the above
(5)
FR2
67. The method used for solving an
assignment problem is to
(a) Obtain balance between total
activities and total resources
(b) Prevent a solution from becoming
degenerate
(c) Provide a means of representing a
dummy problem
(d) None of the above
68. Tow person zero-sum game means
that the
(a) Sum of losses to one player equals
the sum of gains to other
(b) Sum of gains to other
(c) Both (a) the (b)
(d) None of the above
XIX
69. Game theory models are classified by
the
(a) Number of players
(b) Sum of all pay offs
(c) Number of strategic
(d) All of the above
70. A game is said to be fair if –
(a) Both upper and lower values of the
game are same and zero
(b) Upper and lower values of the
game are not equal
(c) Upper value is more than lower
value of the game
(d) None of the above
(6)