Question 1

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 2

Binding constraints have

Accepted Answer

A) zero slack. 
B) negative slack. 
C) positive slack. 
D) surplus resources. 
A) zero slack. 
B) negative slack. 
C) positive slack. 
D) surplus resources.

Question 3

Is the optimal solution to this problem unique,or is there an alternate optimal solution? Explain your reasoning.
MAX 5 X1 + 2 X2
Subject to: 3 X1 + 5 X2 ≤ 15
10 X1 + 4 X2 ≤ 20 X1,X2 ≥ 0

Accepted Answer

Alternate optimal so

Question 4

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 5

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 6

Exhibit 4.1
The following questions are based on the problem below and accompanying Analytic Solver Platform 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):
 $\begin{array}{rrrr}
\text { Week } & \text { TruckingLimits } & \text { Railway Limits } & \text { Air Cargo Limits } \
\hline 1 & 45 & 60 & 15 \
2 & 50 & 55 & 10 \
3 & 55 & 45 & 5 \
\hline \text { Costs } \$ \text { per } 1000 \text { tons) } & \$ 200 & \$ 140 & \$ 400
\end{array}$
 The following is the LP model for this logistics problem.
Let S1U1P1XS1S1P0S1U1B1ij S1U1B0S1U1P1= amount shipped by mode i in week jS1S1P0
where i = 1Truck),2Rail),3Air)and j = 1,2,3
S1U1B1LetS1U1B0S1U1B1 S1U1B0WLS1U1B1ij S1U1B0= weekly limit of mode i in week j as provided in above table)
200XS1U1B111 S1U1B0+ XS1U1B112 S1U1B0+ XS1U1B113S1U1B0)+ 140XS1U1B121 S1U1B0+ XS1U1B122 S1U1B0+ XS1U1B123S1U1B0)+ 500XS1U1B131 S1U1B0+
MIN:
X + X )
Subject to:
32 33
S1U1P1XS1S1P0S1U1B1ij S1U1B0S1U1P1? WL S1S1P0S1U1B1ij S1U1B0S1U1P1for all i and jS1S1P0S1U1P1 S1S1P0Weekly limits by mode
XS1U1B111 S1U1B0+ XS1U1B112 S1U1B0+ XS1U1B113 S1U1B0+ XS1U1B121 S1U1B0+ XS1U1B122 S1U1B0+ XS1U1B123 S1U1B0+ XS1U1B131 S1U1B0+ XS1U1B132 S1U1B0+ XS1U1B133 S1U1B0? 250
Total at end of three weeks
S1U1P1XS1S1P0S1U1B111 S1U1B0S1U1P1+ XS1S1P0S1U1B121 S1U1B0S1U1P1+ XS1S1P0S1U1B131 S1U1B0S1U1P1+ XS1S1P0S1U1B112 S1U1B0S1U1P1+ XS1S1P0S1U1B122 S1U1B0S1U1P1+ XS1S1P0S1U1B132 S1U1B0S1U1P1? 200S1S1P0S1U1P1 S1S1P0Total at end of two weeks S1U1P1XS1S1P0S1U1B111 S1U1B0S1U1P1+ XS1S1P0S1U1B121 S1U1B0S1U1P1+ XS1S1P0S1U1B131 S1U1B0S1U1P1? 120S1S1P0S1U1P1 S1S1P0Total at end of first week
S1U1P1XS1S1P0S1U1B111 S1U1B0S1U1P1+ XS1S1P0S1U1B112 S1U1B0S1U1P1+ XS1S1P0S1U1B113 S1U1B0S1U1P1? 0.45*250S1S1P0S1U1P1 S1S1P0Truck mix requirement
S1U1P1XS1S1P0S1U1B121 S1U1B0S1U1P1+ XS1S1P0S1U1B122 S1U1B0S1U1P1+ XS1S1P0S1U1B123 S1U1B0S1U1P1? 0.40*250S1S1P0S1U1P1 S1S1P0Rail mix requirement
S1U1P1XS1S1P0S1U1B131 S1U1B0S1U1P1+ XS1S1P0S1U1B132 S1U1B0S1U1P1+ XS1S1P0S1U1B133 S1U1B0S1U1P1? 0.15*250S1S1P0S1U1P1 S1S1P0Air mix limit XS1U1B1ij S1U1B0? 0 for all i and j
 \(\begin{array}{rrrrrrr}
&&\text { Final } & \text { Reduced } & \text { Objective } & \text { Allowable } & \text { Allowable } \
&&\text { Value } & \text { Cost } & \text { Coefficient } & \text { Increase } & \text { Decrease }\
\text { Cell } & \text { Name } & & & & \
\hline \$ \mathrm{D} \$ 6 & \text { Week 1 by Truck } & 45 & 0 & 200 & 360 & 1 \mathrm{E}+30 \
\$ \mathrm{E} \$ 6 & \text { Week 1 by Rail } & 60 & 0 & 140 & 360 & 1 \mathrm{E}+30 \
\$ \mathrm{~F} \$ 6 & \text { Week 1 by Air } & 15 & 0 & 500 & 1 \mathrm{E}+30 & 360 \
\$ \mathrm{D} \$ 7 & \text { Week 2 by Truck } & 50 & 0 & 200 & 0 & 1 \mathrm{E}+30 \
\$ \mathrm{E} \$ 7 & \text { Week 2 by Rail } & 55 & 0 & 140 & 0 & 1 \mathrm{E}+30 \
\$ \mathrm{~F} \$ 7 & \text { Week 2 by Air } & 0 & 360 & 500 & 1 \mathrm{E}+30 & 360 \
\$ \mathrm{D} \$ 8 & \text { Week 3 by Truck } & 13 & 0 & 200 & 1 \mathrm{E}+30 & 0 \
\$ \mathrm{E} \$ 8 & \text { Week 3 by Rail } & 12 & 0 & 140 & 60 & 0 \
\$ F \$ 8 & \text { Week 3 by Air } & 0 & 360 & 500 & 1 \mathrm{E}+30 & 360
\end{array}\)
  
-Refer to Exhibit 4.1.Are there alternate optimal solutions to this problem?

Accepted Answer

Cannot tell because we cannot rule out d

Question 7

Exhibit 4.2
The following questions correspond to the problem below and associated Analytic Solver Platform sensitivity report.
Robert Hope received a welcome surprise in this management science class;the instructor has decided to let each person define the percentage contribution to their grade for each of the graded instruments used in the class.These instruments were: homework,an individual project,a mid-term exam,and a final exam.Robert's grades on these instruments were 75,94,85,and 92,respectively.However,the instructor complicated Robert's task somewhat by adding the following stipulations:
· homework can account for up to 25% of the grade,but must be at least 5% of the grade;
· the project can account for up to 25% of the grade,but must be at least 5% of the grade;
· the mid-term and final must each account for between 10% and 40% of the grade but cannot account for more than 70% of the grade when the percentages are combined;and
· the project and final exam grades may not collectively constitute more than 50% of the grade.The following LP model allows Robert to maximize his numerical grade.
Let S1U1P1WS1S1P0S1U1B11 S1U1B0S1U1P1= weight assigned to homework S1S1P0WS1U1B12 S1U1B0= weight assigned to the project WS1U1B13 S1U1B0= weight assigned to the mid-term WS1U1B14 S1U1B0= weight assigned to the final
MAX: S1U1P175WS1S1P0S1U1B11 S1U1B0S1U1P1+ 94WS1S1P0S1U1B12 S1U1B0S1U1P1+ 85WS1S1P0S1U1B13 S1U1B0S1U1P1+ 92WS1S1P0S1U1B14S1U1B0
Subject to: S1U1P1WS1S1P0S1U1B11 S1U1B0S1U1P1+ WS1S1P0S1U1B12 S1U1B0S1U1P1+ WS1S1P0S1U1B13 S1U1B0S1U1P1+ WS1S1P0S1U1B14 S1U1B0S1U1P1= 1S1S1P0
WS1U1B13 S1U1B0+ WS1U1B14 S1U1B0≤ 0.70 WS1U1B13 S1U1B0+ WS1U1B14 S1U1B0≥ 0.50 0.05 ≤ WS1U1B11 S1U1B0≤ 0.25
0.05 ≤ WS1U1B12 S1U1B0≤ 0.25
0.10 ≤ WS1U1B13 S1U1B0≤ 0.40
0.10 ≤ WS1U1B14 S1U1B0≤ 0.40
  
-Refer to Exhibit 4.2.Based on the Analytic Solver Platform sensitivity report information,is there anything Robert can request of his instructor to improve his final grade?

Accepted Answer

Robert can request an increase

Question 8

A spider plot

Accepted Answer

A) is a graphical representation of multiple optimization runs 
B) requires multiple runs of the problem 
C) is computationally expensive to generate for problems with many constraints and variables 
D) all of the above 
A) is a graphical representation of multiple optimization runs 
B) requires multiple runs of the problem 
C) is computationally expensive to generate for problems with many constraints and variables 
D) all of the above

Question 9

How many basic variables are there in a linear programming model which has n variables and m constraints?

Accepted Answer

A) n 
B) m 
C) n + m 
D) n − m 
A) n 
B) m 
C) n + m 
D) n − m

Question 10

When a solution is degenerate the reduced costs for the changing cells

Accepted Answer

A) is always equal to zero. 
B) may not be unique. 
C) may be set to any value the manager needs. 
D) is equal to infinity. 
A) is always equal to zero. 
B) may not be unique. 
C) may be set to any value the manager needs. 
D) is equal to infinity.

Question 11

The allowable decrease 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 decrease given shadow price. 
C) how much resource to use to get the optimal solution. 
D) the amount by which 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 decrease given shadow price. 
C) how much resource to use to get the optimal solution. 
D) the amount by which constraint coefficient can increase without changing the final optimal value.

Question 12

Meaningful Analytic Solver Platform ASP)sensitivity report headings can be defined

Accepted Answer

A) by adding cell notes to spreadsheet cells. 
B) by using the Guess button in the Analytic Solver Platform ASP)dialog box. 
C) by carefully labeling rows and columns in the spreadsheet model. 
D) naming cells in the spreadsheet model. 
A) by adding cell notes to spreadsheet cells. 
B) by using the Guess button in the Analytic Solver Platform ASP)dialog box. 
C) by carefully labeling rows and columns in the spreadsheet model. 
D) naming cells in the spreadsheet model.

Question 13

Consider the formulation below.How many decision variables will be there after the problem has been converted to a standard form?
MAX: 8 X1 + 4 X2
Subject to: 5 X1 + 5 X2 ≤ 20
6 X1 + 2 X2 ≤ 18 X1,X2 ≥ 0

Accepted Answer

A) 4 
B) 2 
C) 3 
D) 5 
A) 4 
B) 2 
C) 3 
D) 5

Question 14

Given an objective function value of 150 and a shadow price for resource 1 of 5,if 10 more units of resource 1 are added assuming the allowable increase is greater than 10),what is the impact on the objective function value?

Accepted Answer

A) increase of 50 
B) increase of unknown amount 
C) decrease of 50 
D) increase of 10 
A) increase of 50 
B) increase of unknown amount 
C) decrease of 50 
D) increase of 10

Question 15

All of the following are true about a variable with a negative reduced cost in a maximization problem except

Accepted Answer

A) its objective function coefficient must increase by that amount in order to enter the basis. 
B) it is at its simple lower bound. 
C) it has surplus resources. 
D) the objective function value will decrease by that value if the variable is increased by one unit. 
A) its objective function coefficient must increase by that amount in order to enter the basis. 
B) it is at its simple lower bound. 
C) it has surplus resources. 
D) the objective function value will decrease by that value if the variable is increased by one unit.

Question 16

Use slack variables to rewrite this problem so that all its constraints are equality constraints.

Accepted Answer

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

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

The Cell Value column in the Solver Answer Report shows

Binding constraints have

Is the optimal solution to this problem unique,or is there an alternate optimal solution? Explain your reasoning. MAX ^{5 X}₁^{+ 2 X}₂ Subject to: ^{3 X}₁^{+ 5 X}₂^{≤ 15} 10 X₁+ 4 X₂≤ 20 X₁,X₂≥ 0

The Simplex method works by first

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

A spider plot

How many basic variables are there in a linear programming model which has n variables and m constraints?

When a solution is degenerate the reduced costs for the changing cells

The allowable decrease for a constraint is

Meaningful Analytic Solver Platform ASP)sensitivity report headings can be defined

Consider the formulation below.How many decision variables will be there after the problem has been converted to a standard form? MAX: ^{8 X}₁^{+ 4 X}₂ Subject to: ^{5 X}₁^{+ 5 X}₂^{≤ 20} 6 X₁+ 2 X₂≤ 18 X₁,X₂≥ 0

Given an objective function value of 150 and a shadow price for resource 1 of 5,if 10 more units of resource 1 are added assuming the allowable increase is greater than 10),what is the impact on the objective function value?

All of the following are true about a variable with a negative reduced cost in a maximization problem except

Use slack variables to rewrite this problem so that all its constraints are equality constraints.

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

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

Data Mining

Time Series Forecasting

Introduction to Simulation Using Analytic Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

Exam 4: Sensitivity Analysis and the Simplex Method

The Cell Value column in the Solver Answer Report shows

Binding constraints have

Is the optimal solution to this problem unique,or is there an alternate optimal solution? Explain your reasoning. MAX 5 X1 + 2 X2 Subject to: 3 X1 + 5 X2 ≤ 15 10 X1 + 4 X2 ≤ 20 X1,X2 ≥ 0

The Simplex method works by first

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

A spider plot

How many basic variables are there in a linear programming model which has n variables and m constraints?

When a solution is degenerate the reduced costs for the changing cells

The allowable decrease for a constraint is

Meaningful Analytic Solver Platform ASP)sensitivity report headings can be defined

Consider the formulation below.How many decision variables will be there after the problem has been converted to a standard form? MAX: 8 X1 + 4 X2 Subject to: 5 X1 + 5 X2 ≤ 20 6 X1 + 2 X2 ≤ 18 X1,X2 ≥ 0

Given an objective function value of 150 and a shadow price for resource 1 of 5,if 10 more units of resource 1 are added assuming the allowable increase is greater than 10),what is the impact on the objective function value?

All of the following are true about a variable with a negative reduced cost in a maximization problem except

Use slack variables to rewrite this problem so that all its constraints are equality constraints.

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

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

Data Mining

Time Series Forecasting

Introduction to Simulation Using Analytic Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

Is the optimal solution to this problem unique,or is there an alternate optimal solution? Explain your reasoning. MAX ^{5 X}₁^{+ 2 X}₂ Subject to: ^{3 X}₁^{+ 5 X}₂^{≤ 15} 10 X₁+ 4 X₂≤ 20 X₁,X₂≥ 0

Consider the formulation below.How many decision variables will be there after the problem has been converted to a standard form? MAX: ^{8 X}₁^{+ 4 X}₂ Subject to: ^{5 X}₁^{+ 5 X}₂^{≤ 20} 6 X₁+ 2 X₂≤ 18 X₁,X₂≥ 0