Chapter: LINEAR PROGRAMMING PROBLEM
101.

Operation research analysis does not

A. predict future operation
B. build more than one model
C. collect the relevant data
D. recommended decision and accept
Answer» A. predict future operation
102.

A constraint in an LP model restricts

A. value of the objective function
B. value of the decision variable
C. use of the available resourses
D. all of the above
Answer» D. all of the above
103.

A feasible solution of LPP

A. must satisfy all the constraints simultaneously
B. need not satisfy all the constraints, only some of them
C. must be a corner point of the feasible region
D. all of the above
Answer» A. must satisfy all the constraints simultaneously
104.

Maximization of objective function in LPP means

A. value occurs at allowable set decision
B. highest value is chosen among allowable decision
C. none of the above
D. all of the above
Answer» B. highest value is chosen among allowable decision
105.

Alternative solution exist in a linear programming problem when

A. one of the constraint is redundant
B. objective function is parallel to one of the constraints
C. two constraints are parallel
D. all of the above
Answer» D. all of the above
106.

The linear function of the variables which is to be maximize or minimize is called

A. constraints
B. objective function
C. decision variable
D. none of the above
Answer» B. objective function
107.

The true statement for the graph of inequations 3x+2y≤6 and 6x+4y≥20 , is

A. both graphs are disjoint
B. both do not contain origin
C. both contain point (1, 1)
D. none of these
Answer» A. both graphs are disjoint
108.

The value of objective function is maximum under linear constraints

A. at the center of feasible region
B. at (0,0)
C. at any vertex of feasible region
D. the vertex which is at maximum distance from (0, 0)
Answer» C. at any vertex of feasible region
109.

A model is

A. an essence of reality
B. an approximation
C. an idealization
D. all of the above
Answer» D. all of the above
110.

The first step in formulating a linear programming problem is

A. identify any upper or lower bound on the decision variables
B. state the constraints as linear combinations of the decision variables
C. understand the problem
D. identify the decision variables
Answer» D. identify the decision variables
111.

Constraints in an LP model represents

A. limititations
B. requirements
C. balancing, limitations and requirements
D. all of above
Answer» D. all of above
112.

The best use of linear programming is to find optimal use of

A. money
B. manpower
C. machine
D. all the above
Answer» D. all the above
113.

Which of the following is assumption of an LP model

A. divisibility
B. proportionality
C. additivity
D. all of the above
Answer» D. all of the above
114.

Before formulating a formal LP model, it is better to

A. express each constraints in words
B. express the objective function in words
C. verbally identify decision variables
D. all of the above
Answer» D. all of the above
115.

Non-negative condition in an LP model implies

A. a positive coefficient of variables in objective function
B. a positive coefficient of variables in any constraint
C. non-negative value of resourse
D. none of the above
Answer» C. non-negative value of resourse
116.

The set of decision variable which satisfies all the constraints of the LPP is called as-----

A. solution
B. basic solution
C. feasible solution
D. none of the above
Answer» A. solution
117.

The intermediate solutions of constraints must be checked by substituting them back into

A. objective function
B. constraint equations
C. not required
D. none of the above
Answer» B. constraint equations
118.

A basic solution is called non-degenerate, if

A. all the basic variables are zero
B. none of the basic variables is zero
C. at least one of the basic variables is zero
D. none of these
Answer» B. none of the basic variables is zero
119.

The graph of x≤2 and y≥2 will be situated in the

A. first and second quadrant
B. second and third quadrant
C. first and third quadrant
D. third and fourth quadrant
Answer» B. second and third quadrant
120.

A solution which satisfies non-negative conditions also is called as-----

A. solution
B. basic solution
C. feasible solution
D. none of the above
Answer» C. feasible solution
121.

A solution which optimizes the objective function is called as ------

A. solution
B. basic solution
C. feasible solution
D. optimal solution
Answer» D. optimal solution
122.

In. L.P.P----

A. objective function is linear
B. constraints are linear
C. both objective function and constraints are linear
D. none of the above
Answer» C. both objective function and constraints are linear
123.

If the constraints in a linear programming problem are changed

A. the problem is to be re-evaluated
B. solution is not defined
C. the objective function has to be modified
D. the change in constraints is ignored.
Answer» A. the problem is to be re-evaluated
124.

Linear programming is a

A. constrained optimization technique
B. technique for economic allocation of limited resources
C. mathematical technique
D. all of the above
Answer» D. all of the above
125.

A constraint in an LP model restricts

A. value of objective function
B. value of a decision variable
C. use of the available resources
D. all of the above
Answer» D. all of the above
126.

The distinguishing feature of an LP model is

A. relationship among all variables is linear
B. it has single objective function & constraints
C. value of decision variables is non-negative
D. all of the above
Answer» A. relationship among all variables is linear
127.

The best use of linear programming technique is to find an optimal use of

A. money
B. manpower
C. machine
D. all of the above
Answer» B. manpower
128.

Which of the following is not a characteristic of the LP

A. resources must be limited
B. only one objective function
C. parameters value remains constant during the planning period
D. the problem must be of minimization type
Answer» D. the problem must be of minimization type
129.

Which of the following is an assumption of an LP model

A. divisibility
B. proportionality
C. additivity
D. all of the above
Answer» D. all of the above
130.

Which of the following is a limitation associated with an LP model

A. the relationship among decision variables in linear
B. no guarantee to get integer valued solutions
C. no consideration of effect of time & uncertainty on lp model
D. all of the above
Answer» D. all of the above
131.

The graphical method of LP problem uses

A. objective function equation
B. constraint equations
C. linear equations
D. all of the above
Answer» D. all of the above
132.

A feasible solution to an LP problem

A. must satisfy all of the problem’s 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
Answer» D. must optimize the value of the objective function
133.

An iso-profit line represents

A. an infinite number of solutions all of which yield the same profit
B. an infinite number of solution all of which yield the same cost
C. an infinite number of optimal solutions
D. a boundary of the feasible region
Answer» D. a boundary of the feasible region
134.

If an iso-profit line yielding the optimal solution coincides with a constaint line, then

A. the solution is unbounded
B. the solution is infeasible
C. the constraint which coincides is redundant
D. none of the above
Answer» A. the solution is unbounded
135.

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
Answer» A. two iso-profit line may be parallel to each other
136.

Constraints in LP problem are called active if they

A. represent optimal solution
B. at optimality do not consume all the available resources
C. both a & b
D. none of the above
Answer» A. represent optimal solution
137.

Mathematical model of Linear Programming is important because

A. It helps in converting the verbal description and numerical data into mathematical expression
B. decision makers prefer to work with formal models.
C. it captures the relevant relationship among decision factors.
D. it enables the use of algebraic techniques.
Answer» A. It helps in converting the verbal description and numerical data into mathematical expression
138.

In graphical method of linear programming problem if the iOS-cost line coincide with a side of region of basic feasible solutions we get

A. Unique optimum solution
B. unbounded optimum solution
C. no feasible solution
D. Infinite number of optimum solutions
Answer» D. Infinite number of optimum solutions
139.

If the value of the objective function 𝒛 can be increased or decreased indefinitely, such solution is called

A. Bounded solution
B. Unbounded solution
C. Solution
D. None of the above
Answer» B. Unbounded solution
140.

For the constraint of a linear optimizing function z=x1+x2 given by x1+x2≤1, 3x1+x2≥3 and x1, x2≥0

A. There are two feasible regions
B. There are infinite feasible regions
C. There is no feasible region
D. None of these
Answer» C. There is no feasible region
141.

If the number of available constraints is 3 and the number of parameters to be optimized is 4, then

A. The objective function can be optimized
B. The constraints are short in number
C. The solution is problem oriented
D. None of these
Answer» B. The constraints are short in number
142.

Non-negativity condition is an important component of LP model because

A. Variables value should remain under the control of the decision-maker
B. Value of variables make sense & correspond to real-world problems
C. Variables are interrelated in terms of limited resources
D. None of the above
Answer» B. Value of variables make sense & correspond to real-world problems
143.

Maximization of objective function in an LP model means

A. Value occurs at allowable set of decisions
B. Highest value is chosen among allowable decisions
C. Neither of above
D. Both a & b
Answer» D. Both a & b
144.

Which of the following is not a characteristic of the LP model

A. Alternative 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.
Answer» A. Alternative courses of action
145.

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 completely used
D. If an optimal solution exists, there will always be at least one at a corner
Answer» A. Every LP problem has an optimal solution
146.

While plotting constraints on a graph paper, terminal points on both the axes are connected by a straight line because

A. The resources are limited in supply
B. The objective function as a linear function
C. The constraints are linear equations or inequalities
D. All of the above
Answer» D. All of the above
Chapter: MATICES AND DETERMINANTS
147.

In graphical method of linear programming problem if the iOS-cost line coincide with a side of region of basic feasible solutions we get

A. unique optimum solution
B. unbounded optimum solution
C. no feasible solution
D. infinite number of optimum solutions
Answer» D. infinite number of optimum solutions
148.

The objective function for a L.P model is 3𝑥1 + 2𝑥2, if 𝑥1 = 20 and 𝑥2 = 30, what is the value of the objective function?

A. 0
B. 50
C. 60
D. 120
Answer» D. 120
149.

If the value of the objective function 𝒛 can be increased or decreased indefinitely, such solution is called

A. bounded solution
B. unbounded solution
C. solution
D. none of the above
Answer» B. unbounded solution
150.

For the constraint of a linear optimizing function z=x1+x2 given by x1+x2≤1, 3x1+x2≥3 and x1, x2≥0

A. there are two feasible regions
B. there are infinite feasible regions
C. there is no feasible region
D. none of these
Answer» C. there is no feasible region
151.

If the number of available constraints is 3 and the number of parameters to be optimized is 4, then

A. the objective function can be optimized
B. the constraints are short in number
C. the solution is problem oriented
D. none of these
Answer» B. the constraints are short in number
152.

While plotting constraints on a graph paper, terminal points on both the axes are connected by a straight line because

A. the resources are limited in supply
B. the objective function as a linear function
C. the constraints are linear equations or inequalities
D. all of the above
Answer» D. all of the above
Chapter: TRANSPORTATION PROBLEM
153.

Operations research is the application of ____________methods to arrive at the optimal Solutions to the problems.

A. economical
B. scientific
C. a and b both
D. artistic
Answer» B. scientific
154.

Operations research was known as an ability to win a war without really going in to ____

A. battle field
B. fighting
C. the opponent
D. both a and b
Answer» D. both a and b
155.

Who defined OR as scientific method of providing execuitive departments with a quantitative basis for decisions regarding the operations under their control?

A. morse and kimball (1946)
B. p.m.s. blackett (1948)
C. e.l. arnoff and m.j. netzorg
D. none of the above
Answer» A. morse and kimball (1946)
156.

What enables us to determine the earliest and latest times for each of the events and activities and thereby helps in the identification of the critical path?

A. programme evaluation
B. review technique (pert)
C. both a and b
D. deployment of resources
Answer» C. both a and b
157.

In Degenerate solution value of objective function _____________.

A. increases infinitely
B. basic variables are nonzero
C. decreases infinitely
D. one or more basic variables are zero
Answer» D. one or more basic variables are zero
158.

OR has a characteristics that it is done by a team of

A. scientists
B. mathematicians
C. academics
D. all of the above
Answer» D. all of the above
159.

Feasible solution satisfies __________

A. only constraints
B. only non-negative restriction
C. [a] and [b] both
D. [a],[b] and optimum solution
Answer» C. [a] and [b] both
160.

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. none of the above
Answer» A. balanced
161.

Which of the following methods is used to verify the optimality of the current solution of the transportation problem

A. least cost method
B. vogel’s approximation method
C. modified distribution method
D. all of the above
Answer» A. least cost method
162.

The degeneracy in the transportation problem indicates that

A. dummy allocation(s) needs to be added
B. the problem has no feasible solution
C. the multiple optimal solution exist
D. a & b but not c
Answer» C. the multiple optimal solution exist
163.

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
Answer» A. satisfy rim conditions
164.

The occurrence of degeneracy while solving a transportation problem means 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
Answer» B. the solution so obtained is not feasible
165.

An alternative optimal solution to a minimization transportation problem exists whenever opportunity cost corresponding to unused route of transportation is:

A. positive & greater than zero
B. positive with at least one equal to zero
C. negative with at least one equal to zero
D. none of the above
Answer» B. positive with at least one equal to zero
166.

One disadvantage of using North-West Corner rule to find 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
Answer» B. it does not take into account cost of transportation
167.

The solution to a transportation problem with ‘m’ rows (supplies) & ‘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
Answer» C. m+n-1
168.

If an opportunity cost value is used 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
Answer» B. most negative number
169.

The large negative opportunity cost value in an unused cell in a transportation table is chosen to improve the current solution because

A. it represents per unit cost reduction
B. it represents per unit cost improvement
C. it ensure no rim requirement violation
D. none of the above
Answer» A. it represents per unit cost reduction
170.

The smallest quantity is chosen at the corners of the closed path with negative sign to be assigned at unused cell because

A. it improve the total cost
B. it does not disturb rim conditions
C. it ensure feasible solution
D. all of the above
Answer» C. it ensure feasible solution
171.

The quantitative approach to decision analysis is a

A. logical approach
B. rational approach
C. scientific approach
D. all of the above
Answer» C. scientific approach
172.

The qualitative approach to decision analysis relies on

A. experience
B. judgement
C. intuition
D. all of the above
Answer» D. all of the above
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