Deck 13: Introduction to Optimization Modeling

Question 1

The optimal solution to any linear programming model is:

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

Answer 1

C

Question 2

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)

Answer 2

C

Question 3

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

Answer 3

B

Question 4

In using Excel to solve linear programming problems,the changing cells represent the:

A)value of the objective function
B)constraints
C)decision variables
D)total cost of the model

Question 5

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

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

Question 6

The solution of a linear programming problem using Microsoft Excel typically involves the following three stages:

A)formulating the problem,invoking Solver,and sensitivity analysis
B)formulating the problem,graphing the problem,and sensitivity analysis
C)the changing cells,the target cells,and the constraints
D)the inputs,the changing cells,and the outputs

Question 7

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

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

Question 8

The equation of the line representing the constraint is:

A)
B)
C)
D)

Question 9

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:

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

Question 10

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 11

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 12

In an optimization model,there can only be one:

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

Question 13

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

A)equal to zero
B)nonnegative
C)nonpositive
D)All of these options

Question 14

Linear programming is a subset of a larger class of models called:

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

Question 15

In using Excel to solve linear programming problems,the target cell represents the:

A)value of the objective function
B)constraints
C)decision variables
D)total cost of the model

Question 16

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 17

The term nonnegativity refers to the condition where:

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

Question 18

Suppose a liquor store sells beer for a net profit of $1 per unit and wine for a net profit of $2 per unit.Let x equal the amount of beer sold and y equal the amount of wine sold.An algebraic formulation of the profit function is:

A)
B)
C)
D)

Question 19

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 20

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

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

Question 21

The equation of the line representing the constraint passes through the points:

A)
B)
C)
D)

Question 22

Related to sensitivity analysis in linear programming,when the profit increases with a unit increase in a resource,this change in profit is referred to as the:

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

Question 23

One of the things that you can do with linear programming and a spreadsheet model is to develop 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 24

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 25

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

Question 26

When there is a problem with Solver being able to find a solution,many times it is an indication of a (n):

A)older version of Excel
B)nonlinear programming problem
C)problem that cannot be solved using linear programming
D)mistake in the formulation of the problem

Question 27

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 28

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 29

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 30

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

Question 31

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 32

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 33

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 34

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

Question 35

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

Question 36

There is often more than one objective in linear programming problems

Question 37

In linear programming we can use the shadow price to calculate increases or decreases in:

A)binding constraints
B)nonbinding constraints
C)values of the decision variables
D)the value of the objective function

Question 38

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

Question 39

In linear programming,sensitivity analysis involves examining how sensitive the optimal solution is to changes in:

A)profit of variables in model
B)cost of variables in model
C)resources available
D)All of these options

Question 40

Linear programming models have three important properties.They are:

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

Question 41

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

Question 42

If the objective function has the equation ,then the slope of the objective function line is 2:

Question 43

If a constraint has the equation ,then the constraint line passes through the points (0,20)and (30,0):

Question 44

If a constraint has the equation ,then the slope of the constraint line is function line is -2:

Question 45

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

Question 46

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 47

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 48

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

Question 49

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

Question 50

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

Question 51

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 52

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 53

If the objective function has the equation ,then the y-intercept of the objective function line is 40:

Question 54

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 55

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 56

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 57

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

Question 58

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

Question 59

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 60

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

Question 61

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 62

(A)What is the objective function in this problem?
(B)What are the constraints in this problem? Write an algebraic expression for each.
(C)Find an optimal solution to the problem using the formulation given in (A)and (B).What is the call plan,and what is the total cost?
(D)Implement the model in (C)in Excel Solver and obtain an answer report.Which constraints are binding on the optimal solution?
(E)Obtain a sensitivity report for the model in (D).If the professor could cut the cost of evening calls from $4 to $3,what would the new calling plan be?
(F)Again using the sensitivity report obtained for (E),suppose the professor could get by with just 100 calls for single females.What would the call costs be in that case? Explain your answer.

Question 63

Find an optimal solution to the problem,assuming that the company will not produce any units in either month that it cannot sell in that month.What is the production plan,and what is the total revenue?

Question 64

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

Question 65

What is the objective function in this problem?

Question 66

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

Question 67

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 like.

Question 68

What are the constraints in this problem?

Question 69

What is the optimal shipping plan? What are the total costs in that case?

Question 70

What is the objective function in this problem?

Question 71

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

Question 72

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

Question 73

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

Question 74

What are the decision variables in this problem?

Question 75

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 76

(A)Formulate a linear programming model that will enable the farmer to determine the number of acres that should be planted cotton and/or corn in order to maximize his profit.
(B)Find an optimal solution to the model in (A)and determine the maximum profit.
(C)Implement the model in (A)in Excel Solver and obtain an answer report.Which constraints are binding on the optimal solution?
(D)Obtain a sensitivity report for the model in (A).How much should the farmer be willing to pay for an additional worker?
(E)Suppose the farmer hires 10 additional workers.Can you use the sensitivity analysis obtained for (D)to determine his expected profit? Would his planting plan change? Explain your answer.
(F)Suppose the farmer now wants to hire 20 additional workers,instead of just 10.Can you use the sensitivity analysis obtained for (D)to determine his expected profit? Explain your answer.

Question 77

What are the constraints in this problem?

Question 78

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

Question 79

What are the decision variables in this problem?

Question 80

What are the decision variables in this problem?