Question 1

To convert=constraints into = constraints the Simplex method adds what type of variable to the constraint?

Accepted Answer

A)  slack 
B)  dummy 
C)  redundant 
D)  spreading 
A)  slack 
B)  dummy 
C)  redundant 
D)  spreading

Question 2

If the shadow price for a resource is 0 and 150 units of the resource are added what happens to the objective function value?

Accepted Answer

A)  increase of 150 
B)  increases more than 0 but less than 150 
C)  no increase 
D)  increases but by an unknown amount 
A)  increase of 150 
B)  increases more than 0 but less than 150 
C)  no increase 
D)  increases but by an unknown amount

Question 3

The allowable increase for a constraint is

Accepted Answer

A)  how many more units of resource to purchase to maximize profits. 
B)  the amount by which the resource can increase given shadow price. 
C)  how much resource to use to get the optimal solution. 
D)  the amount by which the constraint coefficient can increase without changing the final optimal value. 
A)  how many more units of resource to purchase to maximize profits. 
B)  the amount by which the resource can increase given shadow price. 
C)  how much resource to use to get the optimal solution. 
D)  the amount by which the constraint coefficient can increase without changing the final optimal value.

Question 4

The solution to an LP problem is degenerate if

Accepted Answer

A)  the right hand sides of any of the constraints have an allowable increase or allowable decrease of zero. 
B)  the shadow prices of any of the constraints have an allowable increase or allowable decrease of infinity. 
C)  the objective coefficients of any of the variables have an allowable increase or allowable decrease of zero. 
D)  the shadow prices of any of the constraints have an allowable increase or allowable decrease of zero. 
A)  the right hand sides of any of the constraints have an allowable increase or allowable decrease of zero. 
B)  the shadow prices of any of the constraints have an allowable increase or allowable decrease of infinity. 
C)  the objective coefficients of any of the variables have an allowable increase or allowable decrease of zero. 
D)  the shadow prices of any of the constraints have an allowable increase or allowable decrease of zero.

Question 5

The Cell Value column in the Solver Answer Report shows

Accepted Answer

A)  which constraints are binding. 
B)  final (optimal) value assumed by each constraint cell. 
C)  objective function values. 
D)  Right hand sides of constraints. 
A)  which constraints are binding. 
B)  final (optimal) value assumed by each constraint cell. 
C)  objective function values. 
D)  Right hand sides of constraints.

Question 6

The Simplex method works by first

Accepted Answer

A)  identifying any basic feasible solution. 
B)  choosing the largest value for X1. 
C)  setting X1 at one-half of the its maximum value. 
D)  going directly to the optimal solution. 
A)  identifying any basic feasible solution. 
B)  choosing the largest value for X1. 
C)  setting X1 at one-half of the its maximum value. 
D)  going directly to the optimal solution.

Question 7

Exhibit 4.1
The following questions are based on the problem below and accompanying Risk Solver Platform (RSP) sensitivity report.
Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):
 $$\begin{array} { c c c c } 
\text { Week } & \text { Trucking Lanrits } & \text { Railway Limits } & \text { Air Carga Lavits } \
\hline 1 & 45 & 60 & 15 \
2 & 50 & 55 & 10 \
3 & 55 & 45 & 5 \
\hline \text { Costs } ( \$ \text { per } 1000 \text { tors) } & \$ 200 & \$ 140 & \$ 400
\end{array}$$ The following is the LP model for this logistics problem.
    
-Refer to Exhibit 4.1. Should the company negotiate for additional air delivery capacity?

Accepted Answer

No. The shadow price

Question 8

A variable with a final value equal to its simple lower or upper bound and a reduced cost of zero indicates that

Accepted Answer

A)  an alternate optimal solution exists. 
B)  an error in formulation has been made. 
C)  the right hand sides should be increased. 
D)  the objective function needs new coefficients. 
A)  an alternate optimal solution exists. 
B)  an error in formulation has been made. 
C)  the right hand sides should be increased. 
D)  the objective function needs new coefficients.

Question 9

Use slack variables to rewrite this problem so that all its constraints are equality constraints.
 MIN: $\quad 2.5 \mathbf { X } _ { 1 } + 1.5 \mathbf { X } _ { \mathbf { 2 } }$
Subject ta:
$$\begin{array} { l } 
4 X _ { 1 } + 3 X _ { 2} \geq 24 \
2 X _ { 1 } + 4 X _ { 2} \geq 24 \
X _ { 1 }, X _ { 7 } \geq 0
\end{array}$$

Accepted Answer

The answer of Use slack variables to rewrite this problem...

Question 10

Which of the constraints are binding at the optimal solution for the following problem and Risk Solver Platform (RSP) sensitivity output?
 $$\begin{array} { l l } 
\operatorname { MAX } : & 7 \mathbf { X } _ { 1 } + 4 \mathbf { X } _ { \mathbf { 2 } } \
\text { Subject ta: } & 2 \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } \leq 10 \
& \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } \leq 10 \
& 2 \mathbf { X } _ { 1 } + 5 \mathbf { X } _ { \mathbf { 2 } } \leq 40 \
& \mathbf { X } _ { 1 } \mathbf { X } _ { \mathbf { 2 } } \geq \mathbf {0 }
\end{array}$$ $\text {Changing Calls}$
$\begin{array}{llrrrrr}
&&\text { Final} &\text {Reduced }&\text {Objective }&\text {Allowable}&\text { Allowable }\
\text { Cell } & \text { Name } & \text { Value } & \text { Cost } & \text { Coefficient } & \text { Increase } & \text { Decrease } \
\hline \$ \mathrm{~B} \$ 4 & \text { Number to make: } \mathrm{X} 1 &6& 0 & 7& 1& 3 \
\$ \mathrm{C} \$ 4 & \text { Number to make: } \mathrm{X} 2 & 4 & 0 & 4 &3 & 0.5
\end{array}$

$\text {Constraints}$
$\begin{array}{llrrrrr}
&&\text { Final } &\text {Shadow} &\text { Constraint } &\text {Allowable} &\text { Allowable }\
\text { Cell } & \text { Name } & \text { Value } & \text { Price } & \text { R.H. Side } & \text { Increase } & \text { Decrease } \
\hline \$ \mathrm{D} \$ 8 & \text { Used } & 16& 3 & 16 & 4 &2.67 \
\$ \mathrm{D} \$ 9 & \text { Used } & 10 & 1 & 10 & 1 & 2 \
\$ \mathrm{D} \$ 10 & \text { Used } & 32& 0 & 40 & 1 E+30 & 8
\end{array}$

Accepted Answer

The answer of Which of the constraints are binding at...

Question 11

A manager should consider how sensitive the model is to changes in all of the following except

Accepted Answer

A)  differential coefficients. 
B)  objective function coefficients. 
C)  constraint coefficients. 
D)  right-hand side values for constraints. 
A)  differential coefficients. 
B)  objective function coefficients. 
C)  constraint coefficients. 
D)  right-hand side values for constraints.

Question 12

The shadow price of a nonbinding constraint is

Accepted Answer

A)  positive 
B)  zero 
C)  negative 
D)  indeterminate 
A)  positive 
B)  zero 
C)  negative 
D)  indeterminate

Question 13

The difference between the right-hand side (RHS) values of the constraints and the final (optimal) value assumed by the left-hand side (LHS) formula for each constraint is called the slack and is found in the .

Accepted Answer

A)  Status report 
B)  Slack report 
C)  Results report 
D)  Cell Value report 
A)  Status report 
B)  Slack report 
C)  Results report 
D)  Cell Value report

Question 14

A solution to the system of equations using a set of basic variables is called

Accepted Answer

A)  a feasible solution. 
B)  basic feasible solution. 
C)  a nonbasic solution. 
D)  a nonbasic feasible solution 
A)  a feasible solution. 
B)  basic feasible solution. 
C)  a nonbasic solution. 
D)  a nonbasic feasible solution

Question 15

Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited so at most 8 will be produced.
How much can the price of Desks drop before it is no longer profitable to produce them? Base your response on the following Risk Solver Platform (RSP) sensitivity output.
 Laet
$$\begin{array} { l } 
X _ { 1 } = \text { Number of Beds to produce } \
X _ { \mathbf { 2 } } = \text { Number of Desks to produce }
\end{array}$$ The LP model for the problem is
 $\text { MAX: } \quad 30 \mathrm{X}_{1}+40 \mathrm{X}_{2}$
$\begin{array}{l}
\text { Subject to: }\
\begin{array} { l } 
6 X _ { 1 } + 4 X _ { 2 } \leq 36 \text { (carpentry) } \
4 X _ { 1 } + \mathbf { 8 } X _ { 2 } \leq 40 \text { (varnishing } \
X _ { 2 } \leq \mathbf { 8 } \left( \text { demand for } X _ { 2 } \right) \
X _ { 1 } , X _ { 2 } \geq 0
\end{array}
\end{array}$ $\text { Changing Cells}$
$\begin{array}{llrrrrr}
&&\text { Final } & \text { Reduced } & \text { Objective } & \text { Allowable } & \text { Allowable }\

\text { Cell } & \text { Name } & \text { Value } & \text { Cost } & \text { Coefficient } & \text { Increase } & \text { Decrease } \
\hline \$ \text { B } \$ 4 & \text { Number to make: Beds } & 4 & 0 & 30 & 30 & 10 \
\$ \mathrm{\$} \$ 4 & \text { Number to make: Desks } & 3 & 0 & 40 & 20 & 20
\end{array}$

$\text { Constraints }$
$\begin{array}{llrrrrrr}
&&\text { Final } & \text {Shadow } & \text {Constraint } & \text {Allowable } & \text {Allowable }\
\text { Cell } & \text { Name } & \text { Value } & \text { Price } & \text { R.H. Side } & \text { Increase } & \text { Decrease } \
\hline \$ \mathrm{D} \$ 8 & \text { Carpentry Used } & 36 & 2.5 & 36 & 24 & 16 \
\$ \mathrm{D} \$ 9 & \text { Varnishing Used } & 40 & 3.75 & 40 & 26.67 & 16 \
\$ \mathrm{D} \$ 10 & \text { Desk demand Userl } & 3 & 0 & 8 & 1 \mathrm{~E}+30 & 5
\end{array}$

Accepted Answer

The allowa

Question 16

Exhibit 4.1
The following questions are based on the problem below and accompanying Risk Solver Platform (RSP) sensitivity report.
Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):
 $$\begin{array} { c c c c } 
\text { Week } & \text { Trucking Lanrits } & \text { Railway Limits } & \text { Air Carga Lavits } \
\hline 1 & 45 & 60 & 15 \
2 & 50 & 55 & 10 \
3 & 55 & 45 & 5 \
\hline \text { Costs } ( \$ \text { per } 1000 \text { tors) } & \$ 200 & \$ 140 & \$ 400
\end{array}$$ The following is the LP model for this logistics problem.
    
-Refer to Exhibit 4.1. The Week 1 by Truck and Week 1 by Rail constraints each have a shadow price of -360. What do these values imply?

Accepted Answer

Increase the weekly limits on

Question 17

A change in the right hand side of a binding constraint may change all of the following except

Accepted Answer

A)  optimal value of the decision variables 
B)  slack values 
C)  other right hand sides 
D)  objective function value 
A)  optimal value of the decision variables 
B)  slack values 
C)  other right hand sides 
D)  objective function value

Question 18

Risk Solver Platform (RSP) provides all of the following reports except

Accepted Answer

A)  Answer 
B)  Sensitivity 
C)  Cost performance 
D)  Limits 
A)  Answer 
B)  Sensitivity 
C)  Cost performance 
D)  Limits

Question 19

When performing sensitivity analysis, which of the following assumptions must apply?

Accepted Answer

A)  All other coefficients remain constant. 
B)  Only right hand side changes really mean anything. 
C)  The X1 variable change is the most important. 
D)  The non-negativity assumption can be relaxed 
A)  All other coefficients remain constant. 
B)  Only right hand side changes really mean anything. 
C)  The X1 variable change is the most important. 
D)  The non-negativity assumption can be relaxed

Question 20

What are the objective function coefficients for X1 and X2 based on the following Risk Solver Platform (RSP) sensitivity output?
 $\begin{array}{llc}
&\text { Target }\
\text { Cell } & \text { Name } & \text { Value } \
\hline \$ \mathrm{E} \$ 5 & \text {  Unit profit: OBJ. FN. VALUE  } & 58
\end{array}$

$\begin{array}{llrrrrr}
&\text {Adiustable}&&\text {Lower }&\text {Target }&\text {Upper}&\text { Targel}\
\text { Cell } & \text { Name } & \text { Value } & \text { Limit } & \text { Result } & \text { Limit } & \text { Result } \
\hline \$ \text { B } \$ 4 & \text { Number to make: } \mathrm{X} 1 & 6 & 0 &16 & 6& 58\
\$ \text { C } \$ 4 & \text { Number to make } \mathrm{X} 2 & 4 & 6 & 42 & 4 & 58
\end{array}$

Accepted Answer

Coefficien

To convert=constraints into = constraints the Simplex method adds what type of variable to the constraint?

If the shadow price for a resource is 0 and 150 units of the resource are added what happens to the objective function value?

The allowable increase for a constraint is

The solution to an LP problem is degenerate if

The Cell Value column in the Solver Answer Report shows

The Simplex method works by first

A variable with a final value equal to its simple lower or upper bound and a reduced cost of zero indicates that

Use slack variables to rewrite this problem so that all its constraints are equality constraints. MIN: $\quad 2.5 \mathbf { X } _ { 1 } + 1.5 \mathbf { X } _ { \mathbf { 2 } }$ Subject ta: 4+3\geq24 2+4\geq24 ,\geq0

A manager should consider how sensitive the model is to changes in all of the following except

The shadow price of a nonbinding constraint is

The difference between the right-hand side (RHS) values of the constraints and the final (optimal) value assumed by the left-hand side (LHS) formula for each constraint is called the slack and is found in the .

A solution to the system of equations using a set of basic variables is called

A change in the right hand side of a binding constraint may change all of the following except

Risk Solver Platform (RSP) provides all of the following reports except

When performing sensitivity analysis, which of the following assumptions must apply?

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Network Modeling

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

Exam 4: Sensitivity Analysis and the Simplex Method

To convert=constraints into = constraints the Simplex method adds what type of variable to the constraint?

If the shadow price for a resource is 0 and 150 units of the resource are added what happens to the objective function value?

The allowable increase for a constraint is

The solution to an LP problem is degenerate if

The Cell Value column in the Solver Answer Report shows

The Simplex method works by first

A variable with a final value equal to its simple lower or upper bound and a reduced cost of zero indicates that

Use slack variables to rewrite this problem so that all its constraints are equality constraints. MIN: 2.5X1+1.5X2\quad 2.5 \mathbf { X } _ { 1 } + 1.5 \mathbf { X } _ { \mathbf { 2 } }2.5X1​+1.5X2​ Subject ta: 4+3\geq24 2+4\geq24 ,\geq0

A manager should consider how sensitive the model is to changes in all of the following except

The shadow price of a nonbinding constraint is

The difference between the right-hand side (RHS) values of the constraints and the final (optimal) value assumed by the left-hand side (LHS) formula for each constraint is called the slack and is found in the .

A solution to the system of equations using a set of basic variables is called

A change in the right hand side of a binding constraint may change all of the following except

Risk Solver Platform (RSP) provides all of the following reports except

When performing sensitivity analysis, which of the following assumptions must apply?

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Network Modeling

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

Use slack variables to rewrite this problem so that all its constraints are equality constraints. MIN: $\quad 2.5 \mathbf { X } _ { 1 } + 1.5 \mathbf { X } _ { \mathbf { 2 } }$ Subject ta: 4+3\geq24 2+4\geq24 ,\geq0