Deck 13: Introduction to Optimization Modeling

Question 1

All optimization problems include decision variables,one objective function,and two constraints.

Answer 1

False

Question 2

Binding constraints are constraints that hold as an equality.

Answer 2

True

Question 3

Proportionality,additivity,and divisibility are three important properties that LP models possess that distinguish them from general mathematical programming models.

Answer 3

True

Question 4

There are generally two steps in solving an optimization problem: model development and optimization.

Question 5

It is instructive to look at a graphical solution procedure for LP models with three or more decision variables.

Question 6

Suppose the allowable increase and decrease for shadow price for a constraint are $25 (increase)and $10 (decrease).If the right-hand side of that constraint were to increase by $10,the optimal value of the objective function would change.

Question 7

When formulating a linear programming spreadsheet model,there is a set of designated cells that play the role of the decision variables.These are called the objective cells.

Question 8

All linear programming problems should have a unique solution,if they can be solved.

Question 9

A shadow price indicates how much a company would pay for more of a scarce resource.

Question 10

Shadow prices are associated with nonbinding constraints,and show the change in the optimal objective function value when the right side of the constraint equation changes by one unit.

Question 11

Suppose the allowable increase and decrease for an objective coefficient of a decision variable that has a current value of $50 are $25 (increase)and $10 (decrease).If the coefficient were to change from $50 to $60,the optimal value of the objective function would not change.

Question 12

There are two primary ways to formulate a linear programming problem: the traditional algebraic way and with spreadsheets.

Question 13

It is often useful to perform sensitivity analysis to see how,or if,the optimal solution to a linear programming problem changes as we change one or more model inputs.

Question 14

The set of all values of the decision variable cells that satisfy all constraints,not including the nonnegativity constraints,is called the feasible region.

Question 15

Reduced costs indicate how much the objective coefficient of a decision variable that is currently 0 or at its upper bound must change before that the value of that variable changes.

Question 16

When formulating a linear programming spreadsheet model,there is one target (objective)cell that contains the value of the objective function.

Question 17

There is often more than one objective in linear programming problems.

Question 18

In general,the complete solution of a linear programming problem involves three stages: formulating the model,invoking Solver to find the optimal solution,and performing sensitivity analysis.

Question 19

The feasible region in a graphical solution of a linear programming problem will appear as some type of polygon,with lines forming all sides.

Question 20

The divisibility property of LP models simply means that we allow only integer levels of the activities.

Question 21

Suppose an objective function has the equation: .
Then the slope of the objective function line is 2.

Question 22

A rolling planning horizon is a multiperiod model where only the decision in the first period is implemented,and then a new multiperiod model is solved in succeeding periods.

Question 23

Suppose a constraint has this equation: Then the slope of the constraint line is -2.

Question 24

If an LP model has an unbounded solution,then we must have made a mistake - either we have made an input error or we omitted one or more constraints.

Question 25

The additivity property of LP models implies that the sum of the contributions from the various activities to a particular constraint equals the total contribution to that constraint.

Question 26

A feasible solution does not have to satisfy any constraints as long as it is logical.

Question 27

A decision support system is a user-friendly system where an end user can enter inputs to a model and see outputs,but need not be concerned with technical details.

Question 28

Infeasibility refers to the situation in which there are no feasible solutions to the LP model.

Question 29

If a solution to an LP problem satisfies all of the constraints,then it must be feasible.

Question 30

The proportionality property of LP models means that if the level of any activity is multiplied by a constant factor,then the contribution of this activity to the objective function,or to any of the constraints in which the activity is involved,is multiplied by the same factor.

Question 31

In determining the optimal solution to a linear programming problem graphically,if the goal is to maximize the objective,we pull the objective function line down until it contacts the feasible region.

Question 32

The optimal solution to any linear programming model is a corner point of a polygon.

Question 33

A Solver's sensitivity report shows sensitivity to objective coefficients and right sides of the constraints.

Question 34

When the proportionality property of LP models is violated,we generally must use non-linear optimization.

Question 35

A 12-month rolling planning horizon is a single model where the decision in the first period is implemented.

Question 36

When formulating a linear programming spreadsheet model,we specify the constraints in a Solver dialog box,since Excel does not show the constraints directly.

Question 37

Nonbinding constraints will always have slack,which is the difference between the two sides of the inequality in the constraint equation.

Question 38

It helps to ensure that Solver can find a solution to a linear programming problem if the model is well-scaled,that is,if all of the numbers are of roughly the same magnitude.

Question 39

Linear programming problems can always be formulated algebraically,but not always on a spreadsheet.

Question 40

Unboundedness refers to the situation in which the LP model has been formulated in such a way that the objective function is unbounded - that is,it can be made as large (for maximization problems)or as small (for minimization problems)as we wish.

Question 41

A linear programming problem with _____decision variable(s)can be solved by a graphical solution method.

A)two
B)three
C)four
D)five

Question 42

The prototype linear programming problem is to select an optimal mix of products to produce to maximize profit.This type of problem is referred to as the _____ problem.

A)product mix
B)production
C)product/process
D)product scheduling

Question 43

A feasible solution is a solution that satisfies all of the constraints.

Question 44

The value to be optimized in an optimization model (such as profit)is called the objective.

Question 45

Suppose a firm must at least meet minimum expected demands of 60 for product x and 80 of product y.An algebraic formulation of these constraints is

A) .
B) .
C) .
D) .

Question 46

Suppose a company sells two different products,x and y,for net profits of $5 per unit and $10 per unit,respectively.The slope of the line representing the objective function is

A)0.5.
B)-0.5.
C)2.
D)-2.

Question 47

As related to sensitivity analysis in linear programming,when the profit increases with a unit increase in labor,this change in profit is referred to as the

A)add-in price.
B)sensitivity price.
C)shadow price.
D)additional profit.

Question 48

In most cases,when solving linear programming problems,we want the decision variables to be

A)equal to zero.
B)nonnegative.
C)nonpositive.
D)continuous.

Question 49

The optimal solution to any linear programming model is the

A)maximum objective function line.
B)minimum objective function line.
C)corner point of a polygon.
D)maximum or minimum of a parabola.

Question 50

Every linear programming problem involves optimizing a

A)linear regression model subject to several linear constraints.
B)linear function subject to several linear constraints.
C)linear function subject to several non-linear constraints.
D)non-linear function subject to several linear constraints.

Question 51

When using the graphical solution method to solve linear programming problems,the set of points that satisfy all constraints is called the _____ region.

A)optimal
B)feasible
C)constrained
D)logical

Question 52

The most important solution method for linear programming problems is known as the _____ method.

A)spreadsheet
B)solution mix
C)complex
D)simplex

Question 53

An efficient algorithm for finding the optimal solution in a linear programming model is the _____ method.

A)spreadsheet
B)solution mix
C)complex
D)simplex

Question 54

What is the equation of the line representing this constraint?

A)
B)
C)
D)

Question 55

The feasible region in all linear programming problems is bounded by

A)corner points.
B)hyperplanes.
C)an objective line.
D)all of these options.

Question 56

If a manufacturing process takes 3 hours per unit of x and 5 hours per unit of y and a maximum of 100 hours of manufacturing process time are available,then an algebraic formulation of this constraint is

A) .
B) .
C) .
D) .

Question 57

In an optimization model,there can only be one

A)decision variable.
B)constraint.
C)objective function.
D)shadow price.

Question 58

All optimization problems have

A)an objective function and decision variables.
B)an objective function and constraints.
C)decision variables and constraints.
D)an objective function,decision variables and constraints.

Question 59

The term nonnegativity refers to the condition in which the

A)objective function cannot be less than zero.
B)decision variables cannot be less than zero.
C)right hand side of the constraints cannot be greater than zero.
D)reduced cost cannot be less than zero.

Question 60

Linear programming is a subset of a larger class of models called _____ models.

A)mathematical programming
B)mathematical optimality
C)linear regression
D)linear simplex

Question 61

One of the tasks that you can perform with linear programming and a spreadsheet model is developing a user interface to make it easier for someone who is not an expert in using linear programming.The output can be a report that explains the optimal policy in non-technical terms.The type of system being described is called a(n)

A)expert system.
B)decision support system.
C)linear programming support system.
D)production planning system.

Question 62

Consider the following linear programming problem: Maximize: Subject to: The above linear programming problem

A)has only one optimal solution.
B)has more than one optimal solution.
C)exhibits infeasibility.
D)exhibits unboundedness.

Question 63

Conditions that must be satisfied in an optimization model are

A)values of the objective function.
B)constraints.
C)shadow prices.
D)intercepts.

Question 64

The additivity property of linear programming implies that the contribution of any decision variable to the objective is of/on the levels of the other decision variables.

A)Dependent
B)Independent
C)Conditional
D)The sum

Question 65

Linear programming models have three important properties

A)optimality,additivity,and sensitivity.
B)optimality,linearity,and divisibility.
C)divisibility,linearity,and nonnegativity.
D)proportionality,additivity,and divisibility.

Question 66

The divisibility property of linear programming means that a solution can have both

A)integer and noninteger levels of an activity.
B)linear and nonlinear relationships.
C)positive and negative values.
D)revenue and cost information in the model.

Question 67

In some cases,a linear programming problem can be formulated such that the objective can become infinitely large (for a maximization problem)or infinitely small (for a minimization problem).This type of problem is said to be

A)infeasible.
B)inconsistent.
C)unbounded.
D)redundant.

Question 68

Consider the following linear programming problem: Maximize: Subject to: The above linear programming problem

A)has only one optimal solution.
B)has more than one optimal solution.
C)exhibits infeasibility.
D)exhibits unboundedness.

Question 69

Consider the following linear programming problem: Maximize Subject to: The above linear programming problem

A)has only one optimal solution.
B)has more than one optimal solution.
C)exhibits infeasibility.
D)exhibits unboundedness.

Question 70

Consider the following linear programming problem: Minimize: Subject to: The above linear programming problem

A)has only one optimal solution.
B)has more than one optimal solution.
C)exhibits infeasibility.
D)exhibits unboundedness.