Deck 4: Linear Programming Sensitivity Analysis

Question 1

In pricing out a new variable,the worth or value of resources consumed is typically measured by:

A)reduced costs
B)the 100% rule
C)shadow prices
D)slack values
E)surplus values

Answer 1

C

Question 2

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.
$$\begin{array}{l}\text { Formulation }\\\begin{array} { l l } \ { \text { Max } } & 10 \mathrm {~A} + 10 \mathrm {~B} + 10 \mathrm { C } \\\text { Subject to: } & \\& 3 \mathrm {~A} + \mathrm { B } + 5 \mathrm { C } \leq 300 \text { (constraint \#1) } \\& 2 \mathrm {~A} + 4 \mathrm {~B} \leq 400 \text { (constraint \#2) } \\& 4 \mathrm {~A} + 2 \mathrm {~B} + 3.5 \mathrm { C } \leq 200 \text { (constraint \#3) } \\& \mathrm { C } \geq 10 \text { (constraint \#4) } \\& \mathrm { A } , \mathrm { B } , \mathrm { C } \geq 0\end{array}\end{array}$$


-What is the optimal objective function value?

A)925
B)825
C)100
D)92.5
E)none of the above

Answer 2

925

Question 3

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

Answer 3

True

Question 4

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 we force the production of one unit of product A.The new objective function value will be

A)$925
B)$915
C)$935
D)$900
E)Not enough information is provided.

Question 5

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

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

Question 6

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

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

Question 7

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 production manager procures an additional 10 labor hours.What impact will this have on the current optimal objective function value?

A)an increase of $50
B)an increase of $5
C)no change
D)an increase of $35
E)a decrease of $165

Question 8

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

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 9

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

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

Question 10

Surplus is typically associated with which type of constraints?

A)≤
B)≥
C)=
D)≠
E)±

Question 11

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?

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 12

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

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 13

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

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 14

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 production manager has an additional 100 pounds of material 1.What impact will this have on the current optimal objective function value?

A)no change
B)a decrease of $100
C)an increase of $100
D)an increase of $200
E)an increase of $35

Question 15

Sensitivity analysis is analogous to postoptimality analysis

Question 16

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?

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

Question 17

________ can be used to check whether simultaneous changes in RHS or OFC values can be analyzed by using the current sensitivity report.

A)100% rule
B)Pricing out
C)Trial-and-error
D)Graphing
E)none of the above

Question 18

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

Question 19

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?

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

Question 20

Assume that the reduced cost of a decision variable is -$20 for a maximization problem.This implies that:

A)the objective function value will decrease by $20 if we do not produce any units of this product
B)the objective function value will not change if we produce an additional unit of this product
C)the objective function value will increase by $20 if we produce an additional unit of this product
D)the shadow price value will decrease by $20 if we produce an additional unit of this product
E)the objective function value will decrease by $20 if we produce an additional unit of this product

Question 21

The Sensitivity Report typically analyses the impact of simultaneous changes in the objective function coefficients and right-hand side constraint values on the optimal solution.

Question 22

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

Question 23

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

Question 24

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

Question 25

When the Allowable Increase or Allowable Decrease columns for the objective function coefficient of a variable has a value of zero in the Adjustable Cells table,this indicates the presence of a unique solution.

Question 26

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:

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?

Question 27

Use this information to answer the following questions.
An insurance company has three secretaries,A,B,and C that each is capable of processing four different types of insurance claims.The amount of time required by each secretary to process a particular type of a claim is summarized in the following table.

On a typical week,the insurance firm has 5 type 1 claims,4 type 2 claims,2 type 3 claims,and 3 type 4 claims.Each secretary works a maximum of 40 hours per week.The office manager wants to know how many of each type of an insurance claim should be processed by each secretary to minimize the total processing time.

Use the Sensitivity Report to answer the following questions:
a.Suppose that the number of type 1 claims increases to 6 and the number of type 2 claims decreases to 3.What impact would this simultaneous change have on the current optimal objective function value?
b.What is the impact on the current solution and the objective function value if secretary A takes 3 hours to process claim 1 and secretary B takes 5 hours to process claim 1?

Question 28

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

Question 29

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

Question 30

Use this information to answer the following questions.
An insurance company has three secretaries,A,B,and C that each is capable of processing four different types of insurance claims.The amount of time required by each secretary to process a particular type of a claim is summarized in the following table.

On a typical week,the insurance firm has 5 type 1 claims,4 type 2 claims,2 type 3 claims,and 3 type 4 claims.Each secretary works a maximum of 40 hours per week.The office manager wants to know how many of each type of an insurance claim should be processed by each secretary to minimize the total processing time.

Use the Sensitivity Report to answer the following questions:
a.Which constraints are binding?
b.Suppose that secretary A has a total of 45 weekly hours.What impact would this have on the current optimal solution?
c.What is the total number of unused weekly hours for secretary B?
d.Suppose that the number of type 4 claims increases to 4? What impact would this have on the current optimal solution?

Question 31

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

Question 32

Use this information to answer the following questions.
An investment company currently has $1 million available for investment in five different stocks.The company wants to maximize the interest earned over the next year.The five investment possibilities along with the expected interest earned are shown below.To manage risk,the investment firm wishes to have at least 35% of the investment in stocks A and B.Furthermore,no more than 15% of the investment may be in stock E.


Use the Sensitivity Report to answer the following questions:
a.What would be the impact on the optimal allocation if the expected interest earned on stock A decreases to 6%?
b.What would be the impact on the optimal allocation if the expected interest earned on stock A increases to 10%?
c.What should the minimal expected interest earned for stock C be before it would be desirable to invest in this particular stock?
d.What would be the impact on the optimal allocation and the objective function value if the expected interest earned on stock B decreases by 1%?

Question 33

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:

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. )

Question 34

A binding constraint means that the constraint is exactly satisfied,and its left-hand side does not equal its right-hand side.

Question 35

Use this information to answer the following questions.
An investment company currently has $1 million available for investment in five different stocks.The company wants to maximize the interest earned over the next year.The five investment possibilities along with the expected interest earned are shown below.To manage risk,the investment firm wishes to have at least 35% of the investment in stocks A and B.Furthermore,no more than 15% of the investment may be in stock E.


Use the Sensitivity Report to answer the following questions:
a.What is the optimal total expected interest earned for next year?
b.What is the dollar amount that should be invested in each stock?
c.Which constraints are binding? Which constraints are not binding?
d.Is the solution to the problem unique or are there alternate optimal solutions?
e.Does the optimal solution call for investing the entire $1,000,000?

Question 36

The slack of a constraint indicates the amount of a used resource.

Question 37

Use this information to answer the following questions.
An investment company currently has $1 million available for investment in five different stocks.The company wants to maximize the interest earned over the next year.The five investment possibilities along with the expected interest earned are shown below.To manage risk,the investment firm wishes to have at least 35% of the investment in stocks A and B.Furthermore,no more than 15% of the investment may be in stock E.


Use the Sensitivity Report to answer the following questions:
a.Suppose that the amount of money available for investment increases by $50,000.What impact would this have on the current optimal objective function value?
b.Suppose that total investment in stocks A and B must be at least 40% of the total amount available for investment (i.e. ,$400,000).What impact would this have on the current optimal objective function value?
c.Suppose that the total investment in stocks A and be must be at least 30% of the total amount available for investment.What impact would this have on the current optimal objective function value?
d.Assume that no more than 30% of the investment may be in stock E.What impact would this have on the current optimal objective function value?

Question 38

Use this information to answer the following questions.
An insurance company has three secretaries,A,B,and C that each is capable of processing four different types of insurance claims.The amount of time required by each secretary to process a particular type of a claim is summarized in the following table.

On a typical week,the insurance firm has 5 type 1 claims,4 type 2 claims,2 type 3 claims,and 3 type 4 claims.Each secretary works a maximum of 40 hours per week.The office manager wants to know how many of each type of an insurance claim should be processed by each secretary to minimize the total processing time.

Use the Sensitivity Report to answer the following questions:
a.What is the total minimal processing time in hours?
b.Suppose that secretary A can process a type 2 claim in two hours rather than three hours.How would this impact the current optimal solution?
c.Assume that secretary C can process a type 4 claim in 6 hours rather than 5 hours.How would this impact the current optimal solution?
d.Currently,secretary C is not processing any type 4 claims.Suppose that we force secretary four to process one type 4 claim.What impact would this have on the optimal solution?

Question 39

Surplus is typically associated with "≤" constraints.

Question 40

The Reduced Cost may be viewed as the difference between the marginal contribution of a variable and the marginal value of the resources it consumes.

Question 41

Use the information below to answer the following questions.
A real estate developer is planning to build an office complex.Currently,there are three office sizes under consideration: small,medium,and large.Small offices can be rented for $600 per month,medium offices can be rented for $750 per month,and large offices can be rented for $1000 per month.Each small office requires 600 square feet,each medium office requires 800 square feet,and each large office requires 1000 square feet.The current plot of land available to the developer is 100,000 square feet.The developer wants to ensure that the office complex has at least 3 units of each office size.Moreover,zoning restrictions limit the total number of offices to 50.

Use the Sensitivity Report to answer the following questions:
a.How many small,medium,and large offices should the developer build?
b.What is the total optimal monthly revenue?
c.Which constraints are binding? Which constraints are non-binding?
d.How much square footage would remain unused if the developer implements the optimal solution?

Question 42

Use the information below to answer the following questions.
A real estate developer is planning to build an office complex.Currently,there are three office sizes under consideration: small,medium,and large.Small offices can be rented for $600 per month,medium offices can be rented for $750 per month,and large offices can be rented for $1000 per month.Each small office requires 600 square feet,each medium office requires 800 square feet,and each large office requires 1000 square feet.The current plot of land available to the developer is 100,000 square feet.The developer wants to ensure that the office complex has at least 3 units of each office size.Moreover,zoning restrictions limit the total number of offices to 50.

Use the Sensitivity Report to answer the following questions:
a.What would be the impact on the optimal allocation of offices and the objective function value if small offices can be rented for $800 per month rather than $600 per month?
b.What would be the impact on the optimal allocation of offices and the objective function value if medium offices can be rented for $650 per month rather than $750 per month?
c.What would be the impact on the optimal allocation of offices if medium offices can be rented for $1100.00 rather than $750 per month?
d.Is the solution to the problem unique or are there alternate optimal solutions?

Question 43

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?

Question 44

Use the information below to answer the following questions.
A real estate developer is planning to build an office complex.Currently,there are three office sizes under consideration: small,medium,and large.Small offices can be rented for $600 per month,medium offices can be rented for $750 per month,and large offices can be rented for $1000 per month.Each small office requires 600 square feet,each medium office requires 800 square feet,and each large office requires 1000 square feet.The current plot of land available to the developer is 100,000 square feet.The developer wants to ensure that the office complex has at least 3 units of each office size.Moreover,zoning restrictions limit the total number of offices to 50.

Use the Sensitivity Report to answer the following questions:
a.Suppose that the square footage available to the developer increases to 110,000 square feet.What impact would this have on the optimal objective function value?
b.Suppose that the minimal number of small officers that the developer needs to build must be at least 5 offices.What impact would this have on the optimal objective function value?
c.Suppose that the monthly rental of small offices increases to $650,and that the monthly rental of medium offices increases to $800.What impact will this have on the current optimal solution and the objective function value?
d.Suppose that the total number of offices increases to a maximum of 55,and the minimum number of medium offices increases to 5.What impact would this have on the current optimal objective function value?