Question 1

For any constraint,either its slack/surplus value must be zero or its dual price must be zero.

Accepted Answer

A) True 
 B)False

Question 2

Excel's Solver tool has been used in the spreadsheet below to solve a linear programming problem with a minimization objective function and all ≥ constraints.
​
   
a.Give the original linear programming problem.
b.Give the complete optimal solution.

Accepted Answer

a. Min @#LAT-DLM&
s.t. @#LAT-DLM&
@#LAT-DLM&
@#LAT-DLM&
@#LAT-DLM&
b.

Question 3

Use the following Management Scientist output to answer the questions.
MIN 4X1+5X2+6X3
S.T.
Objective Function Value = 400.000
 1) $\mathrm { X } 1 + \mathrm { X } 2 + \mathrm { X } 3  280$
3) $2 X 1 + 4 X 2 + 4 X 3 > 320$ $$\begin{array} { l c c } 
\text { Variable } & \text { Value } & \text { Reduced Cost } \
\mathrm { X } 1 & 0.000 & 1.500 \
\mathrm { X } 2 & 80.000 & 0.000 \
\mathrm { X } 3 & 0.000 & 1.000
\end{array}$$ OBJECTIVE COEFFICIENT RANGES
 $$\begin{array} { l c c } 
\text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \
1 & 5.000 & 0.000 \
2 & 40.000 & 0.000 \
3 & 0.000 & - 1.250
\end{array}$$ RIGHT HAND SIDE RANGES
 $$\begin{array} { l l l l } 
\text { Variable } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \
\text { X1 } & 2.500 & 4.000 & \text { No Upper Limit } \
\text { X2 } & 0.000 & 5.000 & 6.000 \
\text { X3 } & 5.000 & 6.000 & \text { No Upper Limit }
\end{array}$$ $$\begin{array} { l l c l } 
\text { Constraint } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \
1 & 80.000 & 85.000 & \text { No Upper Limit } \
2 & \text { No Lower Limit } & 280.000 & 320.000 \
3 & 280.000 & 320.000 & 340.000
\end{array}$$ 
a.What is the optimal solution,and what is the value of the profit contribution?
b.Which constraints are binding?
c.What are the dual prices for each resource? Interpret.
d.Compute and interpret the ranges of optimality.
e.Compute and interpret the ranges of feasibility.

Accepted Answer

a. @#LAT-DLM&
b. Constraint 3 is binding.
c. Dual

Question 4

A section of output from The Management Scientist is shown here. What will happen to the solution if the objective function coefficient for variable 1 decreases by 20?
$$\begin{array} { l l l l } 
\text { Variable } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \
\hline 1 & 60 & 100 & 120
\end{array}$$

Accepted Answer

A) Nothing.The values of the decision variables,the dual prices,and the objective function will all remain the same. 
B) The value of the objective function will change,but the values of the decision variables and the dual prices will remain the same. 
C) The same decision variables will be positive,but their values,the objective function value,and the dual prices will change. 
D) The problem will need to be resolved to find the new optimal solution and dual price. 
A) Nothing.The values of the decision variables,the dual prices,and the objective function will all remain the same. 
B) The value of the objective function will change,but the values of the decision variables and the dual prices will remain the same. 
C) The same decision variables will be positive,but their values,the objective function value,and the dual prices will change. 
D) The problem will need to be resolved to find the new optimal solution and dual price.

Question 5

If a decision variable is not positive in the optimal solution,its reduced cost is

Accepted Answer

A) what its objective function value would need to be before it could become positive. 
B) the amount its objective function value would need to improve before it could become positive. 
C) zero. 
D) its dual price. 
A) what its objective function value would need to be before it could become positive. 
B) the amount its objective function value would need to improve before it could become positive. 
C) zero. 
D) its dual price.

Question 6

​The cost that varies depending on the values of the decision variables is a

Accepted Answer

A) ​reduced cost. 
B) ​relevant cost. 
C) ​sunk cost. 
D) ​dual cost. 
A) ​reduced cost. 
B) ​relevant cost. 
C) ​sunk cost. 
D) ​dual cost.

Question 7

The 100% Rule compares

Accepted Answer

A) proposed changes to allowed changes. 
B) new values to original values. 
C) objective function changes to right-hand side changes. 
D) dual prices to reduced costs. 
A) proposed changes to allowed changes. 
B) new values to original values. 
C) objective function changes to right-hand side changes. 
D) dual prices to reduced costs.

Question 8

​How can the interpretation of dual prices help provide an economic justification for new technology?

Accepted Answer

The interpretation of dual prices, also

Question 9

There is a dual price for every decision variable in a model.

Accepted Answer

A) True 
 B)False

Question 10

The dual price measures,per unit increase in the right hand side of the constraint,

Accepted Answer

A) the increase in the value of the optimal solution. 
B) the decrease in the value of the optimal solution. 
C) the improvement in the value of the optimal solution. 
D) the change in the value of the optimal solution. 
A) the increase in the value of the optimal solution. 
B) the decrease in the value of the optimal solution. 
C) the improvement in the value of the optimal solution. 
D) the change in the value of the optimal solution.

Question 11

The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the

Accepted Answer

A) optimal solution. 
B) dual solution. 
C) range of optimality. 
D) range of feasibility. 
A) optimal solution. 
B) dual solution. 
C) range of optimality. 
D) range of feasibility.

Question 12

The amount of a sunk cost will vary depending on the values of the decision variables.

Accepted Answer

A) True 
 B)False

Question 13

Which of the following is not a question answered by standard sensitivity analysis information?

Accepted Answer

A) If the right-hand side value of a constraint changes,will the objective function value change? 
B) Over what range can a constraint's right-hand side value without the constraint's dual price possibly changing? 
C) By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility? 
D) By how much will the objective function value change if a decision variable's coefficient in the objective function changes within the range of optimality? 
A) If the right-hand side value of a constraint changes,will the objective function value change? 
B) Over what range can a constraint's right-hand side value without the constraint's dual price possibly changing? 
C) By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility? 
D) By how much will the objective function value change if a decision variable's coefficient in the objective function changes within the range of optimality?

Question 14

Given the following linear program:
The graphical solution to the problem is shown below.From the graph we see that the optimal solution occurs at x1 = 5,x2 = 3,and z = 46.
 $\mathrm{M} A X \quad 5 X_{1}+7 X_{2}$

s.t 
 $\begin{aligned}
   x 1 & \leq 6 \
  2 x_{1}+3 x_{2} & \leq 19 \
   x_{1}+x_{2} & \leq 8 \
   x_{1}, x_{2} & \geq 0
  \end{aligned}$    
a.Calculate the range of optimality for each objective function coefficient.
b.Calculate the dual price for each resource.

Accepted Answer

a. Ranges of optimality: @#LAT-DLM& and

Question 15

​Explain the two interpretations of dual prices based on the accounting assumptions made in calculating the objective
function coefficients.

Accepted Answer

The two interpretations of dual prices a

Question 16

The range of feasibility measures

Accepted Answer

A) the right-hand-side values for which the objective function value will not change. 
B) the right-hand-side values for which the values of the decision variables will not change. 
C) the right-hand-side values for which the dual prices will not change. 
D) each of these choices are true. 
A) the right-hand-side values for which the objective function value will not change. 
B) the right-hand-side values for which the values of the decision variables will not change. 
C) the right-hand-side values for which the dual prices will not change. 
D) each of these choices are true.

Question 17

​A cost that is incurred no matter what values the decision variables assume is

Accepted Answer

A) ​a reduced cost. 
B) ​an optimal cost. 
C) ​a sunk cost. 
D) ​a dual cost. 
A) ​a reduced cost. 
B) ​an optimal cost. 
C) ​a sunk cost. 
D) ​a dual cost.

Question 18

The amount the objective function coefficient of a decision variable would have to improve before that variable would have a positive value in the solution is the

Accepted Answer

A) dual price. 
B) surplus variable. 
C) reduced cost. 
D) upper limit. 
A) dual price. 
B) surplus variable. 
C) reduced cost. 
D) upper limit.

Question 19

The reduced cost for a positive decision variable is 0.

Accepted Answer

A) True 
 B)False

Question 20

In order to tell the impact of a change in a constraint coefficient,the change must be made and then the model resolved.

Accepted Answer

A) True 
 B)False

For any constraint,either its slack/surplus value must be zero or its dual price must be zero.

Excel's Solver tool has been used in the spreadsheet below to solve a linear programming problem with a minimization objective function and all ≥ constraints. a.Give the original linear programming problem. b.Give the complete optimal solution.

A section of output from The Management Scientist is shown here. What will happen to the solution if the objective function coefficient for variable 1 decreases by 20? Variable Lower Limit Current Value Upper Limit 1 60 100 120

If a decision variable is not positive in the optimal solution,its reduced cost is

The cost that varies depending on the values of the decision variables is a

The 100% Rule compares

How can the interpretation of dual prices help provide an economic justification for new technology?

There is a dual price for every decision variable in a model.

The dual price measures,per unit increase in the right hand side of the constraint,

The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the

The amount of a sunk cost will vary depending on the values of the decision variables.

Which of the following is not a question answered by standard sensitivity analysis information?

Explain the two interpretations of dual prices based on the accounting assumptions made in calculating the objective function coefficients.

The range of feasibility measures

A cost that is incurred no matter what values the decision variables assume is

The amount the objective function coefficient of a decision variable would have to improve before that variable would have a positive value in the solution is the

The reduced cost for a positive decision variable is 0.

In order to tell the impact of a change in a constraint coefficient,the change must be made and then the model resolved.

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility Game Theory

Time Series Analysis Forecasting

Intro to Linear Programming

LP Applications

Distribution Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

Exam 8: LP Sensitivity Analysis

For any constraint,either its slack/surplus value must be zero or its dual price must be zero.

Excel's Solver tool has been used in the spreadsheet below to solve a linear programming problem with a minimization objective function and all ≥ constraints. ​ a.Give the original linear programming problem. b.Give the complete optimal solution.

A section of output from The Management Scientist is shown here. What will happen to the solution if the objective function coefficient for variable 1 decreases by 20? Variable Lower Limit Current Value Upper Limit 1 60 100 120

If a decision variable is not positive in the optimal solution,its reduced cost is

​The cost that varies depending on the values of the decision variables is a

The 100% Rule compares

​How can the interpretation of dual prices help provide an economic justification for new technology?

There is a dual price for every decision variable in a model.

The dual price measures,per unit increase in the right hand side of the constraint,

The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the

The amount of a sunk cost will vary depending on the values of the decision variables.

Which of the following is not a question answered by standard sensitivity analysis information?

​Explain the two interpretations of dual prices based on the accounting assumptions made in calculating the objective function coefficients.

The range of feasibility measures

​A cost that is incurred no matter what values the decision variables assume is

The amount the objective function coefficient of a decision variable would have to improve before that variable would have a positive value in the solution is the

The reduced cost for a positive decision variable is 0.

In order to tell the impact of a change in a constraint coefficient,the change must be made and then the model resolved.

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility Game Theory

Time Series Analysis Forecasting

Intro to Linear Programming

LP Applications

Distribution Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

Excel's Solver tool has been used in the spreadsheet below to solve a linear programming problem with a minimization objective function and all ≥ constraints. a.Give the original linear programming problem. b.Give the complete optimal solution.

The cost that varies depending on the values of the decision variables is a

How can the interpretation of dual prices help provide an economic justification for new technology?

Explain the two interpretations of dual prices based on the accounting assumptions made in calculating the objective function coefficients.

A cost that is incurred no matter what values the decision variables assume is