__Note:__We have tried to upload as much as we can, all the question and answers might be shuffled - Please find the answer below each question, some answers might be wrong please review on the last date(some answers might be changed) if you find any of the answer is wrong please comment down below.

__Question 1:__
When using a graphical solution procedure, the region
bounded by the set of constraints is called the

Select one:

A.feasible region

B.infeasible region

C.maximum profit region

D.none of the above

**Correct Answer is : A**

__Question 2:__
An LP problem has a bounded feasible region. If this problem
has an equality constraint, then

Select one:

A.this must be a minimization problem

B.the feasible region must consist of a line segment

C.the problem must be degenerate

D.the problem must have more than one optimal solution

**Correct Answer is : B**

__Question 3:__
If two constraints do not intersect in the positive quadrant
of the graph, then

Select one:

A.The Problem is infeasible

B.The solution is unbounded

C.One of the constraints is redundant.

D.The solution is optimal

**Correct Answer is : B**

__Question 4:__
For a maximization problem, the coefficient for an
artificial variable in the objective function while using two phase simplex
method is

Select one:

A.+1

B.-1

C.+M

D.–M

**Correct Answer is : D**

__Question 5:__
When alternate optimal solutions exist in an LP problem,
then

Select one:

A.the objective function will be parallel to one of the
constraints

B.one of the constraints will be redundant

C.two constraints will be parallel

D.the problem will also be unbounded

**Correct Answer is : A**

__Question 6:__
A optimum solution to an LP problem

Select one:

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 corner point of the feasible region

D.Must optimize the value of the objective function

**Correct Answer is : D**

__Question 7:__
If the constraint has ‘≥’ sign, then we introduce

Select one:

A.Surplus variable

B.Slack variable

C.artificial variable

D.Slack and surplus variables

**Correct Answer is : A**

__Question 8:__
If the feasible region gets larger due to a change in one of
the constraints, the optimal value of the objective function

Select one:

A.must increase or remain the same for a maximization
problem

B.must decrease or remain the same for a maximization
problem

C.must increase or remain the same for a minimization
problem

D.cannot change

**Correct Answer is : A**

__Question 9:__
If there is no feasible region in a LPP, then we say that
the problem has

Select one:

A.Infinite solution

B.No solution

C.Unbounded solution

D.None of these

**Correct Answer is : C**

__Question 10:__
A graphical method should only be used to solve an LP
problem when

Select one:

A.there are only two constraints

B.there are more than two constraints

C.there are only two variables

D.there are more than two variables

**Correct Answer is : C**

__Question 11:__
Which of the following is true with respect to the optimal
solution of an LPP

Select one:

A.Every LPP has an optimal solution

B.Optimal solution of an LPP 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

**Correct Answer is : B**

__Question 12:__
If a linear program is unbounded, the problem probably has
not been formulated correctly. Which of the following would most likely cause
this?

Select one:

A.a constraint was inadvertently omitted

B.an unnecessary constraint was added to the problem

C.the objective function coefficients are too large

D.the objective function coefficients are too small

**Correct Answer is : A**

__Question 13:__
A linear program has been solved and sensitivity analysis
has been performed. The ranges for the objective function coefficients have
been found. For the profit on the upper bound is 80, the lower bound is 60, and
the current value is 75. Which of the following must be true if the profit on
this variable is lowered to 70 and the
optimal? Solution is found?

Select one:

A.a new corner point will become optimal

B.the maximum possible total profit may increase

C.the values for all the decision variables will remain the
same

D.all of the above are possible

**Correct Answer is : C**

__Question 14:__
Maximize z = 3x + 4y subject to the constraints: 4x +
2y 80 , 2x + 5y 180 , x , y ≥ 0

Select one:

A.0 at (0, 0)

B.180 at (20, 30)

C.115 at (35, 2.5)

D.147.5 at (2.5, 35)

**Correct Answer is : D**

__Question 15:__
Which of the following would cause a change in the feasible
region?

Select one:

A.increasing an objective function coefficient in a
maximization problem

B.adding a redundant constraint

C.changing the right-hand side of a no redundant constraint

D.increasing an objective function coefficient in a
minimization problem

**Correct Answer is : C**

__Question 16:__
A constraint that does not affect the feasible solution is a

Select one:

A.non-negative constraint

B.a redundant constraint

C.standard constraint

D.slack constraint

**Correct Answer is : B**

__Question 17:__
Which of the following is a valid objective function
for LPP?

Select one:

A.maximize 6xyz

B.maximize 3x +4y – z

C.minimize 5x2+7y3

D.none of these

**Correct Answer is : B**

__Question 18:__
In the optimal solution to a linear program, there are 20
units of slack for a constraint. From this we know that

Select one:

A.the dual price for this constraint is 20

B.the dual price for this constraint is 0

C.this constraint must be redundant

D.the problem must be a maximization problem

**Correct Answer is : B**

**:**

__Question 19__
Lower and upper bounds in case of an unbounded variable is

Select one:

A.0 and ∞

B.– ∞ and ∞

C.0 and - ∞

D.none of these

**Correct Answer is : A**

__Question 20:__
Mathematical model of LP problem is important because

Select one:

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

**Correct Answer is : A**

__Question 21:__
From a set of equations x + 4y – z = 3 and 5x + 2y + 3z = 4
the basic feasible solution involving x, y is

Select one:

A.(5/9, 11/18, 0)

B.(5/9, 0, 0)

C.(0, 11/18, 0)

D.none of these

**Correct Answer is : A**

__Question 22:__
If a negative value appears in the solution values column of
the simplex table, then

Select one:

A.the solution is optimal

B.the solution is infeasible

C.the solution is unbounded

D.all of the above

**Correct Answer is : B**

__Question 23:__
In solving a linear program, no feasible solution exists. To
resolve this problem we might

Select one:

A.add another variable

B.add another constraint

C.remove or relax a constraint

D.try a different computer program

**Correct Answer is : C**

__Question 24:__
In LP, variables do not have to be integer valued and may
take on any fractional value This assumption is called

Select one:

A.proportionality

B.divisibility

C.additivity

D.certainty

**Correct Answer is : B**

__Question 25:__
The role of artificial variable in the simplex method is

Select one:

A.To find optimal dual prices in the final simplex table

B.to start phases of simple method

C.to aid in finding an initial solution

D.convert inequality constraints into equality

**Correct Answer is : B**

__Question 26:__
Which of the following subroutines does a computer
implementation in LPP by the simplex method use?

Select one:

A.Finding a root of a polynomial

B.Finding the determinant of a matrix

C.Finding the Eigen value of a matrix

D.Solving a system of linear equations

**Correct Answer is : D**

__Question 27:__
A feasible solution to an LP problem

Select one:

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 give the maximum possible profit

**Correct Answer is : A**

__Question 28:__
Let S1- The slack and surplus variables can be unrestricted
in sign

S2 – A basic feasible solution cannot have zero value for
any of the variables

Select one:

A.S1 – True, S2 – True

B.S1 – False, S2 - True

C.S1 – True, S2 – False

D.S1 – False, S2 – False

**Correct Answer is : C**

__Question 29:__
If dual has an unbounded solution, primal has

Select one:

A.Unbounded solution

B.Feasible solution

C.Infeasible solution

D.Optimum solution

**Correct Answer is : D**

__Question 30:__
If a non redundant constraint is removed from an LP problem,
then

Select one:

A.the feasible region will get larger

B.the feasible region will get smaller

C.the problem would become nonlinear

D.the problem would become infeasible

**Correct Answer is : A**

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