Deck 7: Linear Programming Models: Graphical and Computer Methods

Question 1

The rationality assumption implies that solutions need not be in whole numbers (integers).

Answer 1

False

Question 2

In the term linear programming, the word programming comes from the phrase "computer programming."

Answer 2

False

Question 3

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

Answer 3

False

Question 4

An LP formulation typically requires finding the maximum value of an objective while simultaneously maximizing usage of the resource constraints.

Question 5

Resource mix problems use LP to decide how much of each product to make, given a series of resource restrictions.

Question 6

Any time that we have an isoprofit line that is parallel to a constraint, we have the possibility of multiple solutions.

Question 7

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

Question 8

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

Question 9

The term slack is associated with ≥ constraints.

Question 10

One of the assumptions of LP is "proportionality."

Question 11

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

Question 12

The term surplus is associated with ≥ constraints.

Question 13

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

Question 14

One of the assumptions of LP is "simultaneity."

Question 15

The shadow price is the same as the dual price in maximization problems.

Question 16

The existence of non-negativity constraints in a two-variable linear program implies that we are always working in the northwest quadrant of a graph.

Question 17

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

Question 18

Resource restrictions are called constraints.

Question 19

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

Question 20

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

Question 21

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

Question 22

In a minimization problem, the isocost line is used rather than an isoprofit line.

Question 23

The addition of a redundant constraint lowers the isoprofit line.

Question 24

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

A)an objective function
B)a set of constraints
C)non-negativity constraints
D)a redundant constraint

Question 25

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

Question 26

If you enter inequalities such as "≤" directly into your Excel spreadsheet, you do not need to designate them when defining constraints using Solver.

Question 27

In a maximization problem, when one or more of the solution variables and the profit can be made infinitely large without violating any constraints, the linear program has

A)an infeasible solution.
B)an unbounded solution.
C)a redundant constraint.
D)alternate optimal solutions.

Question 28

When using Solver to find a solution for an LP problem, both the left-hand side and the right-hand side of your constraints must be a formula calculated using the cells containing the decision variables.

Question 29

Unlike a maximization problem, a two-variable minimization problem may not be solved graphically.

Question 30

A widely used mathematical programming technique designed to help managers and decision making relative to resource allocation is called

A)linear programming.
B)computer programming.
C)constraint programming.
D)goal programming.

Question 31

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

Question 32

Which of the following is not a property of linear programs?

A)one objective function
B)at least two separate feasible regions
C)alternative courses of action
D)one or more constraints

Question 33

A feasible solution to a linear programming problem

A)must be a corner point of the feasible region.
B)must satisfy all of the problem's constraints simultaneously.
C)need not satisfy all of the constraints, only the non-negativity constraints.
D)must give the maximum possible profit.

Question 34

In a minimization problem, the isocost line slides down and to the left through a feasible region to reflect decreasing costs.

Question 35

When appropriate, the optimal solution to a maximization linear programming problem 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)sliding the constraints to find the greatest point of intersection.

Question 36

The corner point solution method

A)will always provide one, and only one, optimum.
B)will yield different results from the isoprofit line solution method.
C)requires that the profit from all corners of the feasible region be compared.
D)requires that all corners created by all constraints be compared.

Question 37

Infeasibility in a linear programming problem occurs when

A)a constraint is redundant.
B)more than one solution is optimal.
C)the feasible region is unbounded.
D)there is no solution that satisfies all the constraints given.

Question 38

The mathematical theory behind linear programming states that an optimal solution to any problem will lie at a(n)________ of the feasible region.

A)interior point or center
B)maximum point or minimum point
C)corner point or extreme point
D)interior point or extreme point

Question 39

Sensitivity analysis enables us to look at the effects of changing the coefficients in the objective function, one at a time.

Question 40

Constraints do not need to be entered one at a time when using Solver.

Question 41

Sensitivity analyses are used to examine the effects of changes in

A)contribution rates for each variable.
B)degree space.
C)the modeler.
D)the degrees of freedom in the numerator

Question 42

Which of the following is not acceptable as a constraint in a linear programming problem (maximization)? Constraint 1 X + XY + Y ≥ 12
Constraint 2 X - 2Y ≤ 20
Constraint 3 X + 3Y = 48
Constraint 4 X + Y + Z ≤ 150

A)Constraint 1
B)Constraint 2
C)Constraint 3
D)Constraint 4

Question 43

Which of the following is not an assumption of LP?

A)simultaneity
B)certainty
C)proportionality
D)divisibility

Question 44

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 isocost line will change.
C)the optimal solution to the LP is sure to no longer be optimal.
D)the problem will no longer be linear.

Question 45

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

A)unbounded.
B)non-negative.
C)infeasible.
D)redundant.

Question 46

Sensitivity analysis may also be called

A)postoptimality analysis.
B)nonparametric programming.
C)preoptimality analysis.
D)redundancy testing

Question 47

Two models of a product - Regular (X)and Deluxe (Y)- are produced by a company.A linear programming model is used to determine the production schedule.The formulation is as follows:
Maximize profit = 50X + 60Y
Subject to: 8X + 10Y ≤ 800 (labor hours)
X + Y ≤ 120 (total units demanded)
4X + 5Y ≤ 500 (raw materials)
All variable ≥ 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)the fourth constraint

Question 48

When a constraint line bounding a feasible region has the same slope as an isoprofit 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.

Question 49

Consider the following linear programming problem:
Maximize 12X + 10Y
Subject to: 4X + 3Y ≤ 480
2X + 3Y ≤ 360
All variable ≥ 0
The maximum possible value for the objective function is

A)360.
B)480.
C)1520.
D)1560.

Question 50

The difference between the left-hand side and right-hand side of a greater-than-or-equal-to constraint is referred to as

A)surplus.
B)constraint.
C)slack.
D)shadow price.

Question 51

The difference between the left-hand side and right-hand side of a less-than-or-equal-to constraint is referred to as

A)surplus.
B)constraint.
C)slack.
D)shadow price.

Question 52

Consider the following linear programming problem: Maximize 5X + 6Y
Subject to: 4X + 2Y ≤ 420
1X + 2Y ≤ 120
All variable ≥ 0
Which of the following points (X,Y)is not feasible?

A)(50,40)
B)(20,50)
C)(60,30)
D)(90,10)

Question 53

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.

Question 54

Consider the following linear programming problem: Minimize 20X + 30Y
Subject to: 2X + 4Y ≤ 800
6X + 3Y ≥ 300
X, Y ≥ 0
What is the optimum solution to this problem (X,Y)?

A)(0,0)
B)(50,0)
C)(0,100)
D)(400,0)

Question 55

Consider the following linear programming problem:
Maximize 4X + 10Y
Subject to: 3X + 4Y ≤ 480
4X + 2Y ≤ 360
All variable ≥ 0
The feasible corner points are (48,84), (0,120), (0,0), (90,0).What is the maximum possible value for the objective function?

A)1032
B)1200
C)360
D)1600

Question 56

Consider the following linear programming problem: Maximize 20X + 30Y
Subject to: X + Y ≤ 80
8X + 9Y ≤ 600
3X + 2Y ≥ 400
X, Y ≥ 0
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.

Question 57

Consider the following linear programming problem:
Maximize 5X + 6Y
Subject to: 4X + 2Y ≤ 420
1X + 2Y ≤ 120
All variable ≥ 0
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)

Question 58

A constraint with zero slack or surplus is called a

A)nonbinding constraint.
B)resource constraint.
C)binding constraint.
D)nonlinear constraint.

Question 59

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

A)The condition of uncertainty exists.
B)Independence exists for the activities.
C)Proportionality exists in the objective function and constraints.
D)Divisibility does not exist, allowing only integer solutions.

Question 60

Two models of a product - Regular (X)and Deluxe (Y)- are produced by a company.A linear programming model is used to determine the production schedule.The formulation is as follows:
Maximize profit = 50X + 60Y
Subject to: 8X + 10Y ≤ 800 (labor hours)
X + Y ≤ 120 (total units demanded)
4X + 5Y ≤ 500 (raw materials)
All variable ≥ 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)100
C)50
D)120

Question 61

Consider the following linear programming problem: Maximize 20X + 30Y
Subject to: X + Y ≤ 80
12X + 12Y ≤ 600
3X + 2Y ≤ 400
X, Y ≥ 0
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.

Question 62

In order for a linear programming problem to have multiple solutions, the solution must 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.

Question 63

The optimal solution to this linear program is

A)x1 = 34, x2 = 40.
B)x1 = 6, x2 = 11.
C)x1 = 7.33, x2 = 6.
D)x1 = 3, x2 = 6.

Question 64

Consider the following linear programming problem: Maximize 5X + 6Y
Subject to: 4X + 2Y ≤ 420
1X + 2Y ≤ 120
All variables ≥ 0
Which of the following points (X,Y)is in the feasible region?

A)(30,60)
B)(105,5)
C)(0,210)
D)(100,10)

Question 65

A straight line representing all non-negative combinations of X₁ and X₂ for a particular profit level is called a(n)

A)objective line.
B)sensitivity line.
C)profit line.
D)isoprofit line.

Question 66

Which of the following constraints are binding?

A)Extrusion only
B)Packing only
C)Additive only
D)Extrusion and Packaging

Question 67

Consider the following linear programming problem: Maximize 5X + 6Y
Subject to: 4X + 2Y ≤ 420
1X + 2Y ≤ 120
All variables ≥ 0
Which of the following points (X,Y)is feasible?

A)(50,40)
B)(30,50)
C)(60,30)
D)(90,20)

Question 68

What is the increase in the objective value if 2 units of additive are added?

A)0
B)4
C)12
D)16

Question 69

A constraint with positive slack or surplus is called a

A)nonbinding constraint.
B)resource constraint.
C)binding constraint.
D)nonlinear constraint.

Question 70

Which of the following is not an assumption of LP?

A)certainty
B)proportionality
C)divisibility
D)multiplicativity

Question 71

The coefficients of the variables in the constraint equations that represent the amount of resources needed to produce one unit of the variable are called

A)technological coefficients.
B)objective coefficients.
C)shadow prices.
D)dual prices.

Question 72

Consider the following constraints from a linear programming problem: 2X + Y ≤ 200
X + 2Y ≤ 200
X, Y ≥ 0
If these are the only constraints, which of the following points (X,Y)cannot be the optimal solution?

A)(0, 0)
B)(0, 200)
C)(0,100)
D)(100, 0)

Question 73

What is the increase in the objective value if 2 units of packaging are added?

A)11
B)18
C)22
D)36

Question 74

Consider the following linear programming problem: Maximize 12X + 10Y
Subject to: 4X + 3Y ≤ 480
2X + 3Y ≤ 360
All variables ≥ 0
Which of the following points (X,Y)is feasible?

A)(10,120)
B)(120,10)
C)(30,100)
D)(60,90)

Question 75

Consider the following linear programming problem: Maximize 10X + 30Y
Subject to: X + 2Y ≤ 80
8X + 16Y ≤ 640
4X + 2Y ≥ 100
X, Y ≥ 0
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.

Question 76

Which of the following functions is not linear?

A)5X + 3Z
B)3X + 4Y + Z - 3
C)2X + 5YZ
D)Z

Question 77

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.

Question 78

What is the increase in the objective value if 2 units of extrusion are added?

A)3
B)6
C)48
D)96

Question 79

Which of the following is not one of the steps in formulating a linear program?

A)Graph the constraints to determine the feasible region.
B)Define the decision variables.
C)Use the decision variables to write mathematical expressions for the objective function and the constraints.
D)Identify the objective and the constraints.

Question 80

What type of problems use LP to decide how much of each product to make, given a series of resource restrictions?

A)resource mix
B)product restriction
C)resource allocation
D)product mix