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Take Test: Chapter 7

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Question 1

Adding a constraint to a linear programming (maximization) problem may result in, but not belimited to,

a. a decrease in the value of the objective function.b. an increase in the value of the objective function.

c. either an increase or decrease in the value of the objective function.

d. no change in the value of the objective function.

e. either a decrease or no change in the value of the objective function.

1 points

Question 2

In a minimization problem, when one or more of the solution variables and the cost can be madeinfinitely large without violating any constraints, then the linear program has

a. an infeasible solution
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b. an unbounded solution

c. a redundant constraint

d. alternate optimal solutions.

e. none of the above

1 points

Question 3

Infeasibility in a linear programming problem occurs when

a. there is an infinite solution.

b. a constraint is redundant.

c. more than one solution is optimal

d. the feasible region is unbounded

e. there is no solution that satisfies all the constraints given.

1 points

Question 4

Which of the following is not a property of all linear programming problems?

a. the presence of restrictions

b. optimization of some objective

c. a computer program

d. alternate courses of action to choose from

e. usage of only linear equations and inequalities

1 points

Question 5

Management resources that need control include machinery usage, labor volume,money spent, time used, warehouse space used, and material usage.

True

False

1 points

Question 6

Consider the following linear programming problem:

Maximize 20X + 30YSubject to X + Y 808X + 9Y 6003X + 2Y 400

X, Y

0

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This is a special case of a linear programming problem in which

a. there is no feasible solution.

b. there is a redundant constraint

c. there are multiple optimal solutions.d. this cannot be solved graphically.


1 points

Question 7

There are no limitations on the number of constraints or variables that can begraphed to solve an LP problem.

True

False

1 points

Question 8

Which of the following is a basic assumption of linear programming?

a. The condition of uncertainty exists.

b. Proportionality exists in the objective function and constraints.

c. Independence exists for the activities

d. Divisibility exists, allowing only integer solutions.

e. Solutions or variables may take values from to + .

1 points

Question 9

Which of the following is not acceptable as a constraint in a linear programming problem(maximization)?

Constraint 1 X + XY + Y 12Constraint 2 X 2Y 20Constraint 3 X + 3Y = 48Constraint 4 X + Y + Z 150

a. Constraint 1

b. Constraint 2

c. Constraint 3

d. Constraint 4


1 pointsQuestion 10

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In some instances, an infeasible solution may be the optimum found by the cornerpoint method.

True

False

1 points

Question 11

Consider the following linear programming problem:Maximize 5X + 6YSubject to: 4X + 2Y 4201X + 2Y 120all variables 0

Which of the following points (X,Y) is not in the feasible region?

a. (30,30)

b. (60,40)

c. (100,5)

d. (20,40)


1 points

Question 12

An objective function is necessary in a maximization problem but is not required in aminimization problem.

True

False

1 points

Question 13

The graphical solution to a linear programming problem

a. includes the corner point method and the isoprofit line solution method.

b. is useful for four or fewer decision variables.

c. is inappropriate for more than two constraints.

d. is the most difficult approach, but is useful as a learning tool.

e. can only be used if no inequalities exist.

1 points

Question 14

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In order for a linear programming problem to have a unique solution, the solution must exist

a. at the intersection of the non-negativity constraints

b. at the intersection of a non-negativity constraint and a resource constraint.

c. at the intersection of the objective function and a constraint.

d. at the intersection of two or more constraints.


1 points

Question 15

Linear programming has few applications in the real world due to the assumption ofcertainty in the data and relationships of a problem.

True

False

1 points

Question 16


Maximize 12X + 10YSubject to: 4X + 3Y 480

2X + 3Y 360all variables 0

Which of the following points (X,Y) is feasible?

a. (10,120)

b. (120,10)

c. (30,100)

d. (60,90)

e. none of the above1 points

Question 17

The corner point solution method

a. will yield different results from the isoprofit line solution method.

b. requires that the profit from all corners of the feasible region be compared.

c. will provide one, and only one, optimum.

d. requires that all corners created by all constraints be compared.

e. will not provide a solution at an intersection or corner where a non-negativityconstraint is involved

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1 points

Question 18

The condition when there is no solution that satisfies all the constraints is called

a. boundedness

b. redundancy

c. optimality.

d. dependency.


1 points

Question 19


Maximize 12X + 10YSubject to: 4X + 3Y 4802X + 3Y 360all variables 0


a. (10,120)

b. (120,10)

c. (30,100)

d. (60,90)


1 points

Question 20




a. (50,40)

b. (30,50)

c. (60,30)d. (90,20)

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1 points

Question 21

A feasible solution to a linear programming problem

a. must satisfy all of the problem's constraints simultaneously.

b. need not satisfy all of the constraints, only the non-negativity constraints.

c. must be a corner point of the feasible region.

d. must give the maximum possible profit.

1 points

Question 22

Sensitivity analysis enables us to look only at the effects of changing thecoefficients in the objective function.

True

False

1 points

Question 23

Which of the following is not a part of every linear programming problemformulation?

a. an objective function

b. a set of constraints

c. non-negativity constraints

d. a redundant constraint

e. maximization or minimization of a linear function

1 points

Question 24

Industrial applications of linear programming might involve several thousand

variables and constraints.

True

False

1 points

Question 25


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Which of the following points (X,Y) is not feasible?

a. (50,40)

b. (20,50)

c. (60,30)

d. (90,10)


1 points

Question 26

Consider the following linear programming problem:Maximize 20X + 30YSubject to: X + Y 8012X + 12Y 6003X + 2Y 400X, Y 0



b. there is a redundant constraint.

c. there are multiple optimal solutions.

d. this cannot be solved graphically.


1 points

Question 27



Which of the following points (X,Y) is not a feasible corner point?

a. (0,60)

b. (105,0)

c. (120,0)d. (100,10)

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1 points

Question 28

An LP formulation typically requires finding the maximum value of an objective while

simultaneously maximizing usage of the resource constraints.

True

False

1 points

Question 29

Adding a constraint to a linear programming (maximization) problem may result in,

but is not necessarily limited to,

a. a decrease in the value of the objective function.

b. an increase in the value of the objective function.

c. no change to the objective function

d. either (c) or (a) depending on the constraint.

e. either (c) or (b) depending on the constraint.

1 points

Question 30

Two models of a product

Regular (X) and Deluxe (Y)

are produced by a company. A linearprogramming model is used to determine the production schedule. The formulation is as follows:

Maximize profit = 50X + 60YSubject to: 8X + 10Y 800 (labor hours)X + Y 120 (total units demanded)4X +10Y 500 (raw materials)X, Y 0

The optimal solution is X=100, Y=0.

Which of these constraints is redundant?

a. the first constraint

b. the second constraint

c. the third constraint

d. all of the above


1 points

Question 31

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Maximize 12X + 10YSubject to: 4X + 3Y 480


The maximum possible value for the objective function is

a. 360

b. 480

c. 1520.

d. 1560

e. none of the above1 points

Question 32

When two or more constraints conflict with one another, we have a condition calledunboundedness.

True

False

1 points

Question 33

Typical management resources include

a. machinery usage

b. labor volume

c. warehouse space utilization

d. raw material usage

e. all of the above1 points

Question 34

When a constraint line bounding a feasible region has the same slope as anisoprofit line,

a. there may be more than one optimum solution

b. the problem involves redundancy.

c. an error has been made in the problem formulation

d. a condition of infeasibility exists.e. none of the above

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1 points

Question 35

If two corner points tie for the best value of the objective function, then

a. the solution is infeasible

b. there are an infinite number of optimal solutions.

c. the problem is unbounded.

d. the problem is degenerate.


1 points

Question 36

The set of solution points that satisfies all of a linear programming problem'sconstraints simultaneously is defined as the feasible region in graphical linearprogramming.

True

False

1 points

Question 37


Minimize 20X + 30YSubject to 2X + 4Y 8006X + 3Y 300X, Y 0

The optimum solution to this problem occurs at the point (X,Y).

a. (0,0).

b. (50,0).

c. (0,100).

d. (400,0).


1 points

Question 38

The addition of a redundant constraint lowers the isoprofit line.

True

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False

1 points

Question 39

Anytime we have an isoprofit line that is parallel to a constraint, we have thepossibility of multiple solutions

True

False

1 points

Question 40

If the isoprofit line is not parallel to a constraint, then the solution must be unique.

True

False

1 points

Question 41



The maximum possible value for the objective function is

a. 360.

b. 480c. 1520.

d. 1560


1 points

Question 42

Consider the following linear programming problem:Maximize 5X + 6YSubject to: 4X + 2Y 420


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Which of the following points (X,Y) is in the feasible region?

a. (30,60)

b. (105,5)c. (0,210)

d. (100,10)


1 points

Question 43

One converts a minimization problem to a maximization problem by reversing thedirection of all constraints.

True

False

1 points

Question 44

The analytic postoptimality method attempts to determine a range of changes inproblem parameters that will not affect the optimal solution or change thevariables in the basis.

True

False

1 points

Question 45

In a maximization problem, when one or more of the solution variables and the profitcan be made infinitely large without violating any constraints, then the linear

program has

a. an infeasible solution

b. an unbounded solution.

c. a redundant constraint.

d. alternate optimal solutions.


1 points

Question 46

The graphical solution to a linear programming problem

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a. is a useful tool for solving practical problems.

b. is useful for four or less decision variables.

c. is useful primarily in helping one understand the linear programming solution

process.

d. is the most difficult approach.e. can only be used in a maximization problem

1 points

Question 47

One can employ the same algorithm to solve both maximization and minimizationproblems.

True

False

1 points

Question 48

Two models of a product Regular (X) and Deluxe (Y) are produced by a company. A linearprogramming model is used to determine the production schedule. The formulation is as follows:

Maximize profit = 50X + 60 YSubject to: 8X + 10Y 800 (labor hours)X + Y 120 (total units demanded)4X + 5Y 500 (raw materials)all variables 0

The optimal solution is X = 100 Y = 0.

How many units of the regular model would be produced based on this solution?

a. 0

b. 100c. 50

d. 120


1 points

Question 49


Maximize 18X + 36YSubject to: X + Y 80

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6X + 12Y 600X, Y 0




c. there are multiple optimal solutions

d. this cannot be solved graphically


1 points

Question 50

Sensitivity analysis may also be called

a.postoptimality analysis.

b. parametric programming

c. optimality analysis.

d. all of the above


1 points

Question 51

Any linear programming problem can be solved using the graphical solution procedure.

True

False

1 points

Question 52

Changes in the contribution rates in the objective function of an LP may represent

a. changes in the technology used to produce the good.

b. changes in the price for which the product can be sold.

c. changes in government rules and regulations.

d. changes in the raw materials used.


1 points

Question 53

In a linear program, the constraints must be linear, but the objective function may benonlinear.

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True

False

1 pointsQuestion 54

Resource restrictions are called constraints.

True

False

1 points

Question 55



The feasible corner points are (48,84), (0,120), (0,0), (90,0). What is the maximum possiblevalue for the objective function?

a. 1032

b. 1200

c. 360

d. 1600


1 points

Question 56

When appropriate, the optimal solution to a maximization linear programmingproblem can be found by graphing the feasible region and

a. finding the profit at every corner point of the feasible region to see which one

gives the highest value

b. moving the isoprofit lines towards the origin in a parallel fashion until the last

point in the feasible region is encountered

c. locating the point that is highest on the graph

d. none of the above

e. all of the above

1 points

Question 57

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In order for a linear programming problem to have multiple solutions, the solutionmust exist

a. at the intersection of the non-negativity constraints.

b. on a non-redundant constraint parallel to the objective function

c. at the intersection of the objective function and a constraint

d. at the intersection of three or more constraints.


1 points

Question 58

If one changes the contribution rates in the objective function of an LP,

a. the feasible region will change.

b. the slope of the isoprofit or iso-cost line will change.

c. the optimal solution to the LP is sure to no longer be optimal.

d. all of the above


1 points

Question 59

If the addition of a constraint to a linear programming problem does not change thesolution, the constraint is said to be

a. unbounded.

b. non-negative

c. infeasible

d. redundant.

e. bounded.

1 points

Question 60

The simultaneous equation method is

a. an alternative to the corner point method.

b. useful only in minimization methods.

c. an algebraic means for solving the intersection of two or more constraint equations.

d. useful only when more than two product variables exist in a product mix

problem.


1 points

Question 61

In the term linear programming, the word programming comes from the phrasecomputer programming.

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True

False

1 pointsQuestion 62

Which of the following is not acceptable as a constraint in a linear programming problem(minimization)?

Constraint 1 X + Y 12Constraint 2 X - 2Y 20Constraint 3 X + 3Y = 48Constraint 4 X + Y + Z 150Constraint 5 2X - 3Y + Z > 75

a. Constraint 1

b. Constraint 2

c. Constraint 3

d. Constraint 4

e. Constraint 5

1 points

Question 63

Deleting a constraint from a linear programming (maximization) problem may resultin, but is not limited to,

a. a decrease in the value of the objective function.

b. an increase in the value of the objective function.

c. no change to the objective function

d. either (c) or (a) depending on the constraint.

e. either (c) or (b) depending on the constraint.

1 points

Question 64

The graphical method of solution illustrates that the only restriction on a solution isthat the solution must lie along a constraint.

True

False

1 points

Question 65

The solution to a linear programming problem must always lie on a constraint.

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True

False

1 pointsQuestion 66


Maximize 20X + 30YSubject to: X + Y 806X + 12Y 600X, Y 0


a. there is no feasible solution

b. there is a redundant constraint




1 points

Question 67

Removing a constraint from a linear programming (maximization) problem may result in, but not belimited to,

a. a decrease in the value of the objective function

b. an increase in the value of the objective function

c. either an increase or decrease in the value of the objective function.

d. no change in the value of the objective function.

e. either (b) or (d)

1 points

Question 68


Maximize 10X + 30YSubject to X + 2Y 808X + 16Y 6404X + 2Y 100X, Y 0



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1 points

Question 69

Sensitivity analyses are used to examine the effects of changes in

a. contribution rates for each variable

b. technological coefficients

c. available resources

d. all of the above


1 points

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