The document contains 45 multiple choice questions about linear programming problems (LPP), transportation problems, and assignment problems. Some key points covered are: - The feasible region in a graphical LPP solution satisfies all constraints simultaneously. - An LPP deals with problems involving a single objective. - The optimal solution in an LPP maximizes or minimizes the objective function subject to the constraints. - Transportation problems aim to minimize total cost and are a special case of LPPs. - Assignment problems assign origins to destinations at minimum cost when the number of each is equal.

1. Multiple Choice Questions
1.In Graphical solution the feasible region is_____________ .
a. where all the constraints are satisfied simultaneously.
b. any one constraint is satisfied .
c. only the first constraint is satisfied .
d. any one of the above condition.
Answer:A.
2.An LPP has _________.
a. one optimal solutions.
b. two optimal solutions.
c. three .
d. none of these.
Answer:D.
3.An LPP deals with problems involving only_________.
a. single objective.
b. multiple objective.
c. two objective.
d. none of these.
Answer:A.
4.Which of the following is not associated with any LPP_____________.
a. feasible solution .
b. optimum solution.
c.Basic solution .
d. Quadratic equation.
Answer:D.
5.Which of the following is not true about feasibility__________?
a. It cannot be determined in a graphical solution of an LPP.
b. It is independent of the objective function.
c. It implies that there must be a convex region satisfying all the constraints.
d. Extreme points of the convex region gives the optimum solution.
Answer:A
6.In Graphical solution the feasible solution is any solution to a LPP which
satisfies
____________.

2. a. only objective function .
b. non-negativity restriction.
c. only constraint .
d. all the three .
Answer:B.
7.In Graphical solution the redundant constraint is____________.
a. which forms the boundary of feasible region.
b. which do not optimizes the objective function.
c. which does not form boundary of feasible region.
d. which optimizes the objective function.
Answer:C.
8.Optimal solution in an LPP is ___________.
a. which maximizes or minimizes the objective function.
b. which maximizes the objective function.
c. which minimizes the objective function.
d. which satisfies the non negativity restrictions .
Answer:A.
9.Unbounded solution in an LPP is ___________.
a. where the objective function can be decreased indefinitely.
b. which maximizes the objective function.
c. where the objective function can be increased or decreased indefinitely.
d. where the objective function can be increased indefinitely.
Answer:C.
10.The two forms of LPP are _________.
a. standard form and canonical form.
b. standard form and general form.
c. matrix form and canonical form.
d. matrix form and standard form.
Answer:A.
11.The canonical form of LPP if the objective function is of maximization, then all
the
constraints other than non-negativity conditions are __________.
a. greater than type.
b. lesser than type.
c. greater than or equal to type.

3. d.lesser than or equal to type.
Answer:D.
12.The canonical form of LPP if the objective function is of minimization then all
the
constraints other than non-negativity conditions are ___________.
a. greater than type.
b. lesser than type.
c. greater than or equal to type.
d. lesser than or equal to type.
Answer:C.
13.The canonical form of LPP if the objective function is of minimization then
all the constraints other than non-negativity conditions are ________.
a. greater than type.
b.lesser than type.
c.greater than or equal to type.
d. lesser than or equal to type.
Answer: C.
14.The standard form of LPP if the objective function is of minimization then
all the constraints __________.
a. equations.
b. Inequalities.
c. greater than or equal to type
d. lesser than or equal to type
Answer:A.
15.The standard form of LPP if the objective function is of minimization then the
right hand side of the constraints should be__________.
a. positive .
b.negative .
c. non-negative .
d.zero .
Answer:C.
16.Transportation problem is a special class of __________.
a. LPP.
b. assignment problem.
c. none of the two.

4. d. both 1 and 2.
Answer:A.
17.The Objective function of Transportation problem is to________.
a. maximize the total cost.
b.minimize or maximize the total cost.
c.minimize the total cost.
d.total costshould be zero.
Answer:C.
18. In Transportation problem the preferred method of obtaining either optimal or
very close to the optimal solution is _____________.
a. north west corner rule.
b.least costmethod.
c. vogel’s approximation method.
d.simplex method .
Answer:C.
19.In Transportation problem the improved solution of the initial basic feasible
solution is called ___________.
a. basic solution .
b.optimal solution.
c. degenerate solution.
d.non-degenerate solution.
Answer:B.
20.In Transportation problem optimal solution can be verified by using
________.
a. north west corner rule.
b.least costmethod .
c. MODI method.
d.matrix method .
Answer:C.
21.The cells in the Transportation problem can be classified as ________.
a. assigned cells and empty cells .
b. allocated cells and un allocated cells.
c. occupied and unoccupied cells .
d. assigned and unoccupied cells.
Answer:C.

5. 22.In North west corner rule the allocation is done in ________.
a. upper left corner.
b.upperright corner.
c.middle cell in the transportation table.
d.cell with the lowest cost.
Answer:A.
23.In Least costmethod the allocation is done by selecting ___________.
a. upper left corner.
b.upperright corner.
c. middle cell in the transportation table.
d.cell with the lowest cost.
Answer:D.
24.In Transportation problem is said to be balanced if ________.
a. total supply is not equal to total demand .
b.total supply is greater than total demand.
c. total supply is lesser than total demand.
d.total supply is equal to total demand .
Answer:D.
25.In Transportation problem is said to be unbalanced if _________.
a. total supply is not equal to total demand .
b.total supply is greater than total demand.
c. total supply is lesser than total demand.
d.total supply is equal to total demand .
Answer:A.
26.The basic feasible solution to a transportation problem is said to be optimal if
it __________________.
a. maximizes or minimizes the transportation cost.
b.maximizes the transportation cost.
c. minimizes the transportation cost.
d.has degenerate solution.
Answer:C.
27.The necessary and sufficient condition for the existence of a feasible solution
to a transportation problem is a solution that satisfies all the conditions
of_________.

6. a. Supply.
b.Demand.
c. supply and demand.
d.either supply or demand.
Answer:C.
28. Purposeof MODI method is to get__________.
a. degenerate solution.
b.non-degenerate solution.
c. Optimal.
d.basic feasible solution.
Answer:C.
29.In transportation problem the solution is said to non-degenerate solution if
occupied cells is __________.
a.greater than m+n-1.
b.lesser than m+n-1.
c.greater than or equal to m+n-1.
d.lesser than or equal to m+n-1.
Answer:B.
30.In transportation problem the solution is said to degenerate solution if occupied
cells is____________.
a. greater than m+n-1.
b.lesser than m+n-1.
c. greater than or equal to m+n-1.
d.lesser than or equal to m+n-1.
Answer:C.
31.In transportation problem if total supply > total demand we add _________.
a. dummy row with cost0.
b.dummy column with cost0.
c. dummy row with cost1.
d.dummy column with cost1.
Answer:B.
32.In transportation problem if total supply < total demand we add __________.
a. dummy row with cost0.
b.dummy column with cost0.
c. dummy row with cost1.

7. d.dummy column with cost1.
Answer:A.
33.In North west corner rule if the demand in the column is satisfied one must
move
to the ___________.
a. left cell in the next column.
b.right cell in the next row.
c.right cell in the next column.
d.left cell in the next row.
Answer:C.
34.In North west corner rule if the supply in the row is satisfied one must move
_____________.
a. down in the next row.
b.up in the next row.
c. right cell in the next column.
d.left cell in the next row.
Answer:A.
35.Maximization case in transportation problem the objective is to __________.
a. maximize the total profit.
b.minimize the total loss .
c. neither maximize nor minimize.
d.optimal cost.
Answer:A.
36.In Maximization case in transportation problem we convert into minimization
by subtracting all the elements from the ___________.
a. Zero.
b.One.
c. highest element.
d.lowest element.
Answer:C.
37.The application of assignment problems is to obtain _________.
a. only minimum cost.
b.only maximum profit.
c. minimum costor maximum profit .
d.assign the jobs.

8. Answer:C.
38.The assignment problem is said to be unbalanced if __________.
a. number of rows is greater than number of columns.
b.number of rows is lesser than number of columns.
c. number of rows is equal to number of columns.
d.both1 and 2.
Answer:B.
39.The assignment problem is said to be balanced if _________.
a. number of rows is greater than number of columns.
b.number of rows is lesser than number of columns.
c. number of rows is equal to number of columns.
d.if the entry of row is zero.
Answer:C.
40.The assignment problem is said to be balanced if it is __________.
a. square matrix.
b.rectangular matrix.
c. unit matrix .
d.triangular matrix.
Answer:A.
41.In assignment problem if number of rows is greater than column then
_______.
a. dummy column is added .
b.dummy row added .
c. row with cost1 is added.
d.column with cost1 is added.
Answer:A
42.In assignment problem if number of column is greater than row then
_________.
a. dummy column is added .
b.dummy row added .
c. row with cost1 is added.
d.column with cost1 is added.
Answer:B

9. 43.The transportation technique or simplex method cannot be used to solve the
assignment problem becauseof _________ .
a. degeneracy.
b.non-degeneracy.
c. square matrix.
d.any one of the above.
Answer:A.
44.The objective of assignment problem is to assign ___________.
a. number of origins to equal number of destinations at minimum cost.
b.number of origins to equal number of destination at maximum cost.
c. only to maximize cost.
d.only to maximize the profit.
Answer:A.
45. Mean or average number of items served per time period is
called___________.
a. mean service rate.
b..mean arrival rate.
c.average rate service.
d.none of the above.
Answer:A.
46. Mean or average number of arrivals per time period is called__________.
a. mean service rate.
b..mean arrival rate.
c.average rate service.
d.none of the above.
Answer:B.
47. __________refers to the number of customers in the waiting line.
a.service order.
b.queue length.
c.waiting time in queue.
d.none of the above.
Answer:B.
48. The customers are selected for service at random. This is known as the
_________discipline.
a.first-come,first served.

10. b.random service discipline.
c.last come first served.
d.none of the above.
Answer:B.
49. In a linear programming minimization model the objective function
is_________.
a. Minimized.
b. Maximized.
c. minimized or maximized.
d. Standardized.
Answer:B.
50.Which of the following is not associated with any L.P.P_________?
a. feasible solution.
b.optimum solution.
c. Basic solution.
d.quadratic equation.
Answer:D.
51.Linear programming is______________.
a. a constraint optimization model.
b.a constraint decision making model.
c. a mathematical programming model.
d.all the above.
Answer:D.
52.Which of the following is not true about feasibility______________.
a. it cannot be determined in a graphical solution of an L.P.P.
b. it is independent of the objective function.
c. it implies that there must be a convex region satisfying all the constraints.
d. extreme points of the convex region gives the optimum solution.
Answer:A.
53.Graphical method can be used only when the decision variables
is___________.
a. more than 3.
b. more than1.
c. Two.
d. one.

11. Answer:C.
54.In an LPP the Objective function is to be____________.
a. Minimized.
b. maximized.
c. minimized or maximized.
d. Maximin.
Answer:C.
55.The region on the graph sheet with satisfies the constraints including the
non- negativity restrictions is called the _______space.
a. solution.
b.interval.
c. concave.
d.convex.
Answer:A.
56.The __________is the method available for solving an L.P.P.
a. graphical method.
b.least costmethod.
c. MODI method.
d.Hungarian method.
Answer:A.
57.The initial solution of a transportation problem can b 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.no degenerate.
Answer:B.
58.One disadvantage of using north west corner rule to find initial solution to
the transportation problem is that_____________.
a. it is difficult to use.
b. it does not take into accountcostof transportation.
c. it leads to a degenerate initial solution.
d. transportation costis maximum.
Answer:B.

12. 59.The solution of a transportation problem with m rows and n-columns is
feasible if number of positive allocations are__________.
a. m+n.
b.mxn.
c. m+n-1.
d.m+n+1.
Answer:C.
60.When total supply is equal to total demand in a transportation problem, the
problem is said to be__________.
a. Balanced.
b. unbalanced.
c. degenerate.
d. non-degenerate.
Answer:A.
61.Which of the following is methods is used to verify the optimality of the
current solution of the transportation problem__________.
a. least costmethod.
b. vogel’s method.
c. north west corner rule.
d. Modi method.
Answer:D.
62.The method used for solving an assignment problem is
called____________.
a. reduced matrix method.
b. Modi method.
c. hungarian method.
d. graphical method.
Answer:C.
63.The purposeof dummy row or column in 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.any one of the above.
Answer:A.

13. 64.The assignment problem is said to be a balanced one if__________.
a. number of rows is equal to columns.
b. number of rows is greater than columns.
c. number of columns is greater to rows.
d. any one of the above.
Answer:A.
65.An optimal assignment requires that the maximum number of lines that can
be drawn through squares with zero opportunity costbe equal to number
of_________.
a. rows or columns.
b. rows and columns.
c. rows+columns-1.
d. Rows.
Answer:C.
66. The passenger and the train in queueing system describers_________ .
a. Customer and server.
b. Server and customer.
c. Both server.
d. None of these.
Answer:A.
67.If the injured goes to doctorfortreatment then in queueing system the
doctorand injured are respectively____________.
a. Customer and server.
b. Server and customer.
c. Both server.
d. None of these.
Answer:B.
68.Under the exponential assumptions the probability that an event occurin
sufficient small interval is ____________.
a .Greater than one.
b .Less than one.
c .Equals to one.
d .None of these.
Answer: A .
69.Under the exponential assumption, the probability that an event will

14. occurin sufficient small interval is________________.
a. Always positive.
b. Always negative.
c. Always Zero .
d. None of these.
Answer: B.
70.The interarrival time is 10 minutes the arrival rate is ________.
a.8.
b.1/10.
c.3.
d.2.
Answer:A .
71.Let p be the probability that an arrival occurs in Δ t =0 under exponential
assumptions___________.
a. 0≤p≤1.
b. 0<p≤1.
c. 0<p<1.
d. 0≤1<1.
Answer: B .
72.The mean and standard deviation of exponential distribution are _________.
a. Equal.
b. Mean>s. d.
c. Mean< s. d.
d. None of these.
Answer: C .
73.Let q be the probability that no arrival occurin Δt=0 under exponential
assumption is ________.
a. 0≤q≤1.
b. 0<q<1.
c. 0≤q<1.
d. 0<q≤1.
Answer:A .
74. If the rate of birth is 12 per minute. Then the average number of birth per
year is __________.
a.43800.

15. b.45000.
c.40000.
d.None of these .
Answer: A.
75. If the interarrival time is exponential with mean 1/ ‫ג‬ eht
Number of arrivals in (0,t) is___________.
a. Poissondistributed.
b. Exponential distributed .
c. Binomial distributed .
d. None of these.
Answer:B .
76. The inter departure time , correspondingto truncated Poissondistribution in a
pure death model is ___________.
a. Exponential distributed .
b. Poissondistributed.
c. Binomial distributed.
d. None of these.
Answer:A .
77.The arrival of customer(with no departure) in system, in queueing theory can
be stated as__________.
a. The pure birth process.
b. The pure death process.
c. The birth death process.
d. None of these.
Answer: A.
78.The withdrawal of items from certain in ventory without refilling in queueing
systems can be stated as __________.
a. The pure birth process.
b. The pure death process.
c. The birth death process.
d. None of these .
Answer: B .
79.The arrival and departure of quests in a hotel in queueing systems can be ststed
as
________.

16. a. The pure birth process.
b. The pure death process.
c. The birth death process.
d. None of these.
Answer: C .
80.In certain situation the customer arrives from one gate and departure takes from
another gate. This situation of incoming and outgoing can be stated as _________.
a. The pure death process.
b. The pure birth process.
c. The birth-death process.
d. None of these.
Answer: C .
81.There are N inventories in the system, one by one all the inventories are
consumed with replacing the inventories. This process is stated as_____________.
a. The pure birth process.
b. The pure death process.
c. The birth death process.
d. None of these.
Answer: A .
82.The departure and arrivals in queuing system are normally considered
respectively M/M/1 the arrival and departure distribution are_____________.
a. Both Markovian .
b. Binomial.
c. General.
d. None of these.
Answer:A .
83.In queue description M/M/1, the number of servers are _____________.
a. 1.
b. M.
c. 2.
d. None of these.
Answer: A .
84.Consider the situation, when no server is working, then the number of
customers
in the system are___________.

17. a. Equal to number of customers in queue.
b. More than number of customers in queue.
c. Less than number of customers in queue.
d. None of these.
Answer: A .
85.On a certain day, number of customers in a system are 20,and number of
customer in service are 12,the number of customers waiting for service are
________.
a. 10.
b. 8.
c. 20.
d. None of these.
Answer: B .
86.Let C be the expected number of servers in the system ,Cˉ the expected number
of serves not busy and C the expected number of servers busy then__________.
a. C=C-C.
b. C=C+C.
c. C=C/C.
d. C=C/C.
Answer: A .
87. Let λ be an arrival rate of customer in a system, μ be an service rate of the
system then the expected number of busy servers are _______.
a. λ/ μ .
b. λ+ μ .
c. λ μ.
d. None of these.
Answer: A .
88. The expected waiting time in the system is 10 minutes, and expected waiting
time in the queue is 5 minutes then the service rate is _______.
a.1 /10.
b.1/5.
c. 5.
d. 0.
Answer: B.

18. 89.The traffic intensity for M/M/1 system is given by ________.
a. p=λ/μ.
b. p=μ/λ.
c. p=λμ.
d. None of these.
Answer: A .
90.For M/M/1 queueing system, the expected number of customers in the system
are ___.
a. L =p/1-p.
b. L=1-p/p.
c. L=1-p.
d. None of these.
Answer: A .
91. For M/M/1 queueing system, the expected number of customers in the system
are_______.
a. L= λ / μ-λ.
b. L= λ-μ / λ.
c. L= μ / μ-λ.
d. None of these .
Answer: A .
92. For M/M/1 queueing system if arrival rate is 10 customers/day and service rate
is 30 customers per day then expected number of customers in the queue on a
certain day is _________.
a. 1/3.
b. 1/6.
c. 6.
d. None of these.
Answer: A .
93. If arrival rate is 15 customers per minute and service rate is 30 customers per
minute, then for M/M/1 queueing system, its traffic intensity is given
by__________.
a. ½ .
b. 2.
c. 4.
d. None of these.

19. Answer: A .
94. If arrival rate is 20 customers/perweek and service rate is 50 customers/week,
then the expected number of busy servers for M/M/1 queueing system are
_________.
a. 2/5.
b. 5/2.
c. 5 .
d. None of these .
Answer: A .
95.For M/M/1 system, the expected waiting time in the queue is ________.
a. λ / μ .
b. λ / μ(μ-λ).
c. λ / μ-λ.
d. None of these.
Answer: B .
96.For M/M/1 model the expected number of busy servers are equal to_______.
a. Traffic intensity p .
b. Arrival rate λ .
c. Service rate μ .
d. None of these .
Answer: A .
97.For M/M/1 model the probability that there is no customer in the system is
________.
a. 1.5 .
b. 2.
c.3.
d.5.
Answer: A .
98.For M/M/1/N queue modules, if P n is the number of customers in the system
then ________.
a. P n=0 for n>N.
b. Pn≠0 for n>N .
c. P n=1 for n>N.
d. None of these.
Answer: A .

20. 99. When p=1, for M/M/1/N queueing system, expected number of customers in
the
system are__________ .
a. N/2.
b. N/6.
c. N .
d. None of these.
Answer: A .
100. For M/M/1/N system, the expected waiting time in the system for p=1 is
________.
a. W=N/2 λ .
b. W=N/2 .
c. W=1/λ .
d. None of these .
Answer: A .
101.Any feasible solution which optimize the objective function of general linear
programming problem is called an _________________ to that linear
programming problem.
a.Initial basic feasible solution
b.Optimal feasible solution.
c.Bounded solution.
d.None of the above.
Answer : B.
103.To find dual of linear programming problem,the primal must be in
___________?
a.Standard form.
b.Canonical form.
c.With <=, =, >= signs.
d.None of the above.
Answer: B.
105.If the dual of the linear programming problem have a finite optimal
solution,then primal process________?
a.Finite optimal solution.
b.Unbounded solution.

21. c.No solution.
d.Infinite solution.
Answer: A.
106.Inthe optimal table of a transportation problem a zero in the south_west corner
rule shows that____________?
a.An alternate optimal solution exists.
b.The optimal solution is degenerated.
c.(a) and (b) both true.
d.None of these.
Answer: B.
107.In transportation problem,one of the dual variable is assigned an arbitrary
value, because_______________?
a.Then a solution is obtained immediately.
b.One of the constrains is redundant in a transportation problem.
c.This facilitates construction of the loop.
d.None of these.
Answer: B.
108.In transportation problem,if two dual variable is assigned an arbitrary value,
then_______________?
a.The method will yield correct solution.
b.The method will not yield correctsolution.
c.Both cases possible.
d.None is true.
Answer: B.
109.If the value of the objective function is unbounded in primal,then the dual of
the problem have__________?
a.Infesible solution.
b.Fesible solution.
c.Bounded solution.
d.Unbounded solution.
Answer: A.
110.The north-west corner rule is used to find _____________?
a.Initial fesible solution.
b.An optimal solution.
c.Non optimal solution.

22. d.None of these.
Answer: A.
111.Which of the following is an integer linear programming problem?
a.Transportation problem.
b.Assignment problem.
c.Primal dual problem.
d.All of these.
Answer: B.
112.In a balanced transportation problem with m orgins and n destinations the
number of linearly independent constrain is_____________?
a.m+n.
b.m+n+1.
c.m+n-1.
d.None of these.
Answer: C.
113.Assingment problem is a ______________?
a.Integer programming problem.
b.Non-integer programming problem.
c.Non-linear programming problem.
d.None of these.
Answer: A.
114.An assignment problem is a _____________?
a.Transportation problem.
b.Non-integer programming problem.
c.Non-linear programming problem.
d.None of these.
Answer: A.
115.The linear programming problem in which all or some of the variables,are
constrained to assume non-negative integer values is reffered as______________?
a.Integer programming problem.
b.Dynamic programming problem.
c.Non-linear programming problem.
d.None of these.
Answer: A.

23. 116.Allocation model involves the assignment of a number of jobs to the same
number of men is called______________.
a.transportation problem.
b.assignment problem.
c.decision theory.
d.simulation.
Answer: B.
117._________ modelare related to decision making under conditions of certainty,
risk and uncertainty.
a.transportation problem.
b.assignment problem.
c.decision theory.
d.simulation.
Answer: C.
118.Waiting line theory deals with the situation in which ________formed.
a.queue.
b.assignment.
c.transportation.
d.none of the above.
Answer: A.
120. Service location decisions typically attempt to__________ .
a. minimize costs.
b. consider global implications.
c. decrease labor costs.
d. none of the above.
Answer: C.
134. The transportation method, when applied to location analysis__________.
a. minimizes total fixed costs.
b. minimizes total production and transportation costs.
c. maximizes revenues.
d. minimizes the movement of goods.
Answer: B.

24. 143. Which of the following is a location analysis technique typically employed by
a service
organization?
a. purchasing power analysis.
b. linear programming.
c. queuing theory.
d. crossovercharts.
Answer: C.
145. Location analysis techniques typically employed by manufacturing
organizations include
_______________________ .
a. transportation method.
b. queuing theory.
c. correlation analysis and traffic counts.
d. simulation.
Answer: A.
148.The customers are selected for service at random. This is known as the
_________discipline.
a.first-come,first served.
b.random service discipline.
c.last come first served.
d.none of the above.
Answer:B.
149.__________refers to the number of customers in the waiting line.
a.service order.
b.queue length.
c.waiting time in queue.
d.none of the above.
Answer:B.
150.Mean or average number of arrivals per time period is called__________.
a. mean service rate.
b..mean arrival rate.
c.average rate service.
d.none of the above.
Answer:B.