Linear Algebra and Optimization- MCQS

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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 : A

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 : B

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 : B

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 : D

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 : C

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 : C

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 : D

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 : C

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