Question 1

Impact of changes in RHS values of constraints is typically measured by the:

Accepted Answer

A) reduced cost 
B) RHS allowable increase value 
C) RHS allowable decrease value 
D) shadow price 
E) objective function coefficients 
A) reduced cost 
B) RHS allowable increase value 
C) RHS allowable decrease value 
D) shadow price 
E) objective function coefficients

Question 2

A company can decide how many additional labor hours to acquire for a given week.Subcontractors will only work a maximum of 20 hours a week.The company must produce at least 200 units of product A,300 units of product B,and 400 units of product C.In 1 hour of work,worker 1 can produce 15 units of product A,10 units of product B,and 30 units of product C.Worker 2 can produce 5 units of product B,20 units of product B,and 35 units of product C.Worker 3 can produce 20 units of product A,15 units of product B,and 25 units of product C.Worker 1 demands a salary of $50/hr,worker 2 demands a salary of $40/hr,and worker 3 demands a salary of $45/hr.The company must choose how many hours they should hire from each worker to meet their production requirements and minimize labor cost.The sensitivity report is displayed below.
   
Answer the following questions:
a.How much of products A,B,and C should be produced?
b.Which constraints are binding? Which constraints are non-binding?
c.If constraint 2 is relaxed by one unit,how will the objective value be affected?

Accepted Answer

a.0 units of Product A,9.23 units of Pro

Question 3

Assume that the shadow price of a non-binding "≤" constraint is 5.This implies that:

Accepted Answer

A) if the right-hand side value of the constraint increases by 1 unit,the objective function value will increase by 5 units 
B) if the right-hand side value of the constraint increases by 1 unit,the objective function value will decrease by 5 units 
C) if the right-hand side value of the constraint increases by 1 unit,the objective function value will remain unchanged 
D) if the right-hand side value of the constraint decreases by 1 unit,the objective function value will increase by 5 units 
E) if the objective function coefficient increases by 1 unit,the shadow price will increase by 5 units 
A) if the right-hand side value of the constraint increases by 1 unit,the objective function value will increase by 5 units 
B) if the right-hand side value of the constraint increases by 1 unit,the objective function value will decrease by 5 units 
C) if the right-hand side value of the constraint increases by 1 unit,the objective function value will remain unchanged 
D) if the right-hand side value of the constraint decreases by 1 unit,the objective function value will increase by 5 units 
E) if the objective function coefficient increases by 1 unit,the shadow price will increase by 5 units

Question 4

The 100% Rule can be using to measure simultaneous changes in which of the following?

Accepted Answer

A) OFC values 
B) RHS values 
C) LHS values 
D) both A and B 
E) A,B,and C 
A) OFC values 
B) RHS values 
C) LHS values 
D) both A and B 
E) A,B,and C

Question 5

Use this information,along with its associated Sensitivity Report,to answer the following questions.
A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits.Production requirements for the products are shown in the following table.
 $$\begin{array} { | c | c | c | c | } 
\hline \underline { \text { Product } } & \frac { \text { Material 1 } } { ( \mathrm { lbs } ) } & \frac { \text { Material 2 } } { ( \mathrm { lbs } . ) } & \text { Labor (hours) } \
\hline \underline { \underline { \mathrm { A } } } & \underline { 3 } & \underline { 2 } & \underline { 4 } \
\hline \underline { \mathrm { B } } & \underline { 1 } & \underline { 4 } & \underline { 2 } \
\hline \underline { \mathrm { C } } & \underline { 5 } & \underline { \text { none } } & \underline { 3.5 } \
\hline
\end{array}$$ 
Material 1 costs $7 a pound,material 2 costs $5 a pound,and labor costs $15 per hour.Product A sells for $101 a unit,product B sells for $67 a unit,and product C sells for $97.50 a unit.Each week there are 300 pounds of material 1;400 pounds of material 2;and 200 hours of labor.The output of product A should not be more than one-half of the total number of units produced.Moreover,there is a standing order of 10 units of product C each week.
 $$\begin{array}{l}
\text { Formulation }\
\begin{array} { l l } 
\ { \text { Max } } & 10 \mathrm {~A} + 10 \mathrm {~B} + 10 \mathrm { C } \
\text { Subject to: } & \
& 3 \mathrm {~A} + \mathrm { B } + 5 \mathrm { C } \leq 300 \text { (constraint \#1) } \
& 2 \mathrm {~A} + 4 \mathrm {~B} \leq 400 \text { (constraint \#2) } \
& 4 \mathrm {~A} + 2 \mathrm {~B} + 3.5 \mathrm { C } \leq 200 \text { (constraint \#3) } \
& \mathrm { C } \geq 10 \text { (constraint \#4) } \
& \mathrm { A } , \mathrm { B } , \mathrm { C } \geq 0
\end{array}
\end{array}$$ 
  
-Suppose that the objective function coefficient for product C increases by $8.What impact will this have on the current values of the optimal solution?

Accepted Answer

A) No change. 
B) Current solution will change. 
C) Solution will become infeasible. 
D) Solution will become unbounded. 
E) Not enough information is provided. 
A) No change. 
B) Current solution will change. 
C) Solution will become infeasible. 
D) Solution will become unbounded. 
E) Not enough information is provided.

Question 6

A constraint has a slack of 5 units.This implies that:

Accepted Answer

A) this constraint has exceeded its minimal requirement by 5 units 
B) this constraint has consumed 5 units of its resource 
C) this constraint has a surplus of 5 units 
D) this constraint is binding 
E) this constraint has 5 units of its resource unconsumed 
A) this constraint has exceeded its minimal requirement by 5 units 
B) this constraint has consumed 5 units of its resource 
C) this constraint has a surplus of 5 units 
D) this constraint is binding 
E) this constraint has 5 units of its resource unconsumed

Question 7

The information provided in the Sensitivity Report assumes that we are considering a change to only a single input data value.

Accepted Answer

A) True 
 B)False

Question 8

As long as the objective function coefficient for a given variable increases within its allowable increase,the current optimal solution remains the same

Accepted Answer

A) True 
 B)False

Question 9

A constraint has a surplus of 10 units.This implies that:

Accepted Answer

A) this constraint has exceeded its minimal requirement by 10 units 
B) this constraint has consumed 10 units of its resource 
C) this constraint has a slack of 10 units 
D) this constraint has 10 units of its resource unconsumed 
E) this constraint is binding 
A) this constraint has exceeded its minimal requirement by 10 units 
B) this constraint has consumed 10 units of its resource 
C) this constraint has a slack of 10 units 
D) this constraint has 10 units of its resource unconsumed 
E) this constraint is binding

Question 10

Optimal solutions to linear programming problems are found under probabilistic assumptions.

Accepted Answer

A) True 
 B)False

Question 11

The presence of zeros in the Allowable Increase or Allowable decrease columns for objective function values indicates:

Accepted Answer

A) alternate optimal solution 
B) unbounded solution 
C) redundant constraint 
D) infeasible solution 
E) unique solution 
A) alternate optimal solution 
B) unbounded solution 
C) redundant constraint 
D) infeasible solution 
E) unique solution

Question 12

The slack values in the Answer Report can refer to either slack or surplus values based on the type of the inequality.

Accepted Answer

A) True 
 B)False

Question 13

A constraint right-hand side value is increased within its allowable increase value.The shadow price for this constraint will still be valid.

Accepted Answer

A) True 
 B)False

Question 14

The Sensitivity Report has two parts: one part deals with objective function coefficient changes,and the other part deals with constraint coefficient changes.

Accepted Answer

A) True 
 B)False

Question 15

Use this information to answer the following questions.
A company can ship its product from any of its three factories,F1,F2,and F3,to any of its retail outlets,R1,R2,and R3.The capacity,demand,and shipping cost information is provided as follows:
 $\begin{array}{ll}
\text { Demand (units) } & \text { Capacity (units) } \
\text { R1:300 } & \text { F1:250 } \
\text { R2: } 500 & \text { F2: } 350 \
\text { R3:200 } & \text { F3:400 }
\end{array}$

$\begin{array}{l}
\text { Shipping Cost/unit (\$) }\
\begin{array}{lll}
&\mathrm{R} 1 & \mathrm{R} 2& \mathrm{R} 3 \
F1&1&3&2\
F2&3 & 4 & 2 \
F3&2 & 2 & 3
\end{array}
\end{array}$
 
The company wants to come up with an optimal shipping strategy that will allow it to minimize its total shipping cost.
  
-Use the Sensitivity Report to answer the following questions:
a.Suppose that the shipping cost per unit for variable X1 (i.e. ,route F1-R1)increases to $2.00.What impact will this have on the current optimal solution and the objective function value?
b.Suppose that the shipping cost per unit for variable X6 (i.e. ,route F2-R3)increases by $2.00 to $5.00.What impact will this have on the current optimal solution and the objective function value?
c.Suppose that the factory constraints and the retail outlet constraints become "≤".What would the optimal solution and the objective function coefficient be? (Hint: The answer to this question is not given in the Sensitivity Report. )

Accepted Answer

a.The current optimal solution will rema

Question 16

A given constraint has 40 unused hours.The shadow price for this resource would most likely be zero.

Accepted Answer

A) True 
 B)False

Question 17

Use this information,along with its associated Sensitivity Report,to answer the following questions.
A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits.Production requirements for the products are shown in the following table.
 $$\begin{array} { | c | c | c | c | } 
\hline \underline { \text { Product } } & \frac { \text { Material 1 } } { ( \mathrm { lbs } ) } & \frac { \text { Material 2 } } { ( \mathrm { lbs } . ) } & \text { Labor (hours) } \
\hline \underline { \underline { \mathrm { A } } } & \underline { 3 } & \underline { 2 } & \underline { 4 } \
\hline \underline { \mathrm { B } } & \underline { 1 } & \underline { 4 } & \underline { 2 } \
\hline \underline { \mathrm { C } } & \underline { 5 } & \underline { \text { none } } & \underline { 3.5 } \
\hline
\end{array}$$ 
Material 1 costs $7 a pound,material 2 costs $5 a pound,and labor costs $15 per hour.Product A sells for $101 a unit,product B sells for $67 a unit,and product C sells for $97.50 a unit.Each week there are 300 pounds of material 1;400 pounds of material 2;and 200 hours of labor.The output of product A should not be more than one-half of the total number of units produced.Moreover,there is a standing order of 10 units of product C each week.
 $$\begin{array}{l}
\text { Formulation }\
\begin{array} { l l } 
\ { \text { Max } } & 10 \mathrm {~A} + 10 \mathrm {~B} + 10 \mathrm { C } \
\text { Subject to: } & \
& 3 \mathrm {~A} + \mathrm { B } + 5 \mathrm { C } \leq 300 \text { (constraint \#1) } \
& 2 \mathrm {~A} + 4 \mathrm {~B} \leq 400 \text { (constraint \#2) } \
& 4 \mathrm {~A} + 2 \mathrm {~B} + 3.5 \mathrm { C } \leq 200 \text { (constraint \#3) } \
& \mathrm { C } \geq 10 \text { (constraint \#4) } \
& \mathrm { A } , \mathrm { B } , \mathrm { C } \geq 0
\end{array}
\end{array}$$ 
  
-Which constraints are binding?

Accepted Answer

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

Question 18

Use this information,along with its associated Sensitivity Report,to answer the following questions.
A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits.Production requirements for the products are shown in the following table.
 $$\begin{array} { | c | c | c | c | } 
\hline \underline { \text { Product } } & \frac { \text { Material 1 } } { ( \mathrm { lbs } ) } & \frac { \text { Material 2 } } { ( \mathrm { lbs } . ) } & \text { Labor (hours) } \
\hline \underline { \underline { \mathrm { A } } } & \underline { 3 } & \underline { 2 } & \underline { 4 } \
\hline \underline { \mathrm { B } } & \underline { 1 } & \underline { 4 } & \underline { 2 } \
\hline \underline { \mathrm { C } } & \underline { 5 } & \underline { \text { none } } & \underline { 3.5 } \
\hline
\end{array}$$ 
Material 1 costs $7 a pound,material 2 costs $5 a pound,and labor costs $15 per hour.Product A sells for $101 a unit,product B sells for $67 a unit,and product C sells for $97.50 a unit.Each week there are 300 pounds of material 1;400 pounds of material 2;and 200 hours of labor.The output of product A should not be more than one-half of the total number of units produced.Moreover,there is a standing order of 10 units of product C each week.
 $$\begin{array}{l}
\text { Formulation }\
\begin{array} { l l } 
\ { \text { Max } } & 10 \mathrm {~A} + 10 \mathrm {~B} + 10 \mathrm { C } \
\text { Subject to: } & \
& 3 \mathrm {~A} + \mathrm { B } + 5 \mathrm { C } \leq 300 \text { (constraint \#1) } \
& 2 \mathrm {~A} + 4 \mathrm {~B} \leq 400 \text { (constraint \#2) } \
& 4 \mathrm {~A} + 2 \mathrm {~B} + 3.5 \mathrm { C } \leq 200 \text { (constraint \#3) } \
& \mathrm { C } \geq 10 \text { (constraint \#4) } \
& \mathrm { A } , \mathrm { B } , \mathrm { C } \geq 0
\end{array}
\end{array}$$ 
  
-By how much would the profit contribution of product A has to increase before it will be profitable to produce A?

Accepted Answer

A) $20 
B) $0 
C) $1E+30 
D) $132.5 
E) $10 
A) $20 
B) $0 
C) $1E+30 
D) $132.5 
E) $10

Question 19

Use this information to answer the following questions.
A company can ship its product from any of its three factories,F1,F2,and F3,to any of its retail outlets,R1,R2,and R3.The capacity,demand,and shipping cost information is provided as follows:
 $\begin{array}{ll}
\text { Demand (units) } & \text { Capacity (units) } \
\text { R1:300 } & \text { F1:250 } \
\text { R2: } 500 & \text { F2: } 350 \
\text { R3:200 } & \text { F3:400 }
\end{array}$

$\begin{array}{l}
\text { Shipping Cost/unit (\$) }\
\begin{array}{lll}
&\mathrm{R} 1 & \mathrm{R} 2& \mathrm{R} 3 \
F1&1&3&2\
F2&3 & 4 & 2 \
F3&2 & 2 & 3
\end{array}
\end{array}$
 
The company wants to come up with an optimal shipping strategy that will allow it to minimize its total shipping cost.
  
-Use the Sensitivity Report to answer the following questions:
a.Will any of the retail outlets experience any shortages in meeting their demand requirements if we implement the optimal solution?
b.Will any of the factories have any remaining quantities of the product if we implement the optimal solution?
c.What is the total minimal shipping cost?

Accepted Answer

Formulation:
Let X1=no.of units shipped

Question 20

A change in the right-hand side value of a binding constraint usually affects the size of the feasible region.

Accepted Answer

A) True 
 B)False

Impact of changes in RHS values of constraints is typically measured by the:

Assume that the shadow price of a non-binding "≤" constraint is 5.This implies that:

The 100% Rule can be using to measure simultaneous changes in which of the following?

A constraint has a slack of 5 units.This implies that:

The information provided in the Sensitivity Report assumes that we are considering a change to only a single input data value.

As long as the objective function coefficient for a given variable increases within its allowable increase,the current optimal solution remains the same

A constraint has a surplus of 10 units.This implies that:

Optimal solutions to linear programming problems are found under probabilistic assumptions.

The presence of zeros in the Allowable Increase or Allowable decrease columns for objective function values indicates:

The slack values in the Answer Report can refer to either slack or surplus values based on the type of the inequality.

A constraint right-hand side value is increased within its allowable increase value.The shadow price for this constraint will still be valid.

The Sensitivity Report has two parts: one part deals with objective function coefficient changes,and the other part deals with constraint coefficient changes.

A given constraint has 40 unused hours.The shadow price for this resource would most likely be zero.

A change in the right-hand side value of a binding constraint usually affects the size of the feasible region.

Introduction to Managerial Decision Making

Linear Programming Models: Graphical and Computer Methods

Linear Programming Modeling Applications with Computer Analyses in Excel

Transportation, Assignment, and Network Models

Integer, Goal, and Nonlinear Programming Models

Project Management

Decision Analysis

Queuing Models

Simulation Modeling

Forecasting Models

Inventory Control Models

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Exam 4: Linear Programming Sensitivity Analysis

Impact of changes in RHS values of constraints is typically measured by the:

Assume that the shadow price of a non-binding "≤" constraint is 5.This implies that:

The 100% Rule can be using to measure simultaneous changes in which of the following?

A constraint has a slack of 5 units.This implies that:

The information provided in the Sensitivity Report assumes that we are considering a change to only a single input data value.

As long as the objective function coefficient for a given variable increases within its allowable increase,the current optimal solution remains the same

A constraint has a surplus of 10 units.This implies that:

Optimal solutions to linear programming problems are found under probabilistic assumptions.

The presence of zeros in the Allowable Increase or Allowable decrease columns for objective function values indicates:

The slack values in the Answer Report can refer to either slack or surplus values based on the type of the inequality.

A constraint right-hand side value is increased within its allowable increase value.The shadow price for this constraint will still be valid.

The Sensitivity Report has two parts: one part deals with objective function coefficient changes,and the other part deals with constraint coefficient changes.

A given constraint has 40 unused hours.The shadow price for this resource would most likely be zero.

A change in the right-hand side value of a binding constraint usually affects the size of the feasible region.

Introduction to Managerial Decision Making

Linear Programming Models: Graphical and Computer Methods

Linear Programming Modeling Applications with Computer Analyses in Excel

Transportation, Assignment, and Network Models

Integer, Goal, and Nonlinear Programming Models

Project Management

Decision Analysis

Queuing Models

Simulation Modeling

Forecasting Models

Inventory Control Models

Filters