Question 1

The Simplex method uses which of the following values to determine if the objective function value can be improved?

Accepted Answer

A)   shadow price
B)   target value
C)   reduced cost
D)   basic costE) A) and D)
F) All of the above

Question 2

The slope of the level curve for the objective function value can be changed by

Accepted Answer

A)   increasing the value of the decision variables.
B)   doubling all the coefficients in the objective function.
C)   increasing the right hand sides of constraints.
D)   changing a coefficient in the objective function.E) A) and B)
F) B) and C)

Question 3

Why might a decision maker prefer a solution in the interior of the feasible region of a linear programming problem?

Accepted Answer

A)   Such a solution has a better objective function value than any other solution
B)   Such a solution is likely to remain feasible if some of the coefficients in the problem change
C)   The decision maker is not sure if he/she wants to maximize or minimize the objective
D)   Such a solution has more binding constraintsE) A) and B)
F) B) and D)

Question 4

Risk Solver Platform (RSP)  provides sensitivity analysis information on all of the following except the

Accepted Answer

A)   range of values for objective function coefficients which do not change optimal solution.
B)   impact on optimal objective function value of changes in constrained resources.
C)   impact on optimal objective function value of changes in value of decision variables.
D)   impact on right hand sides of changes in constraint coefficients.E) A) and D)
F) None of the above

Question 5

What is the value of the objective function if X1 is set to 0 in the following Limits Report?   Target  Cell  Name  Value $E$5 Unit profit: Total Profit: 3200\begin{array}{llc}&	ext { Target }\	ext { Cell } & 	ext { Name } & 	ext { Value } \\hline \$ \mathrm{E} \$ 5 & 	ext { Unit profit: Total Profit: } & 3200\end{array} Cell $E$5​ Target  Name  Unit profit: Total Profit: ​ Value 3200​​

AdiustableLower Target Upper Targel Cell  Name  Value  Limit  Result  Limit  Result $ B $4 Number to make: X180080079.99999993200$ C $4 Number to make X220024203200\begin{array}{llrrrrr}&	ext {Adiustable}&&	ext {Lower }&	ext {Target }&	ext {Upper}&	ext { Targel}\	ext { Cell } & 	ext { Name } & 	ext { Value } & 	ext { Limit } & 	ext { Result } & 	ext { Limit } & 	ext { Result } \\hline \$ 	ext { B } \$ 4 & 	ext { Number to make: } \mathrm{X} 1 & 80 & 0 & 800 & 79.9999999 & 3200 \\$ 	ext { C } \$ 4 & 	ext { Number to make } \mathrm{X} 2 & 20 & 0 & 24 & 20 & 3200\end{array} Cell $ B $4$ C $4​Adiustable Name  Number to make: X1 Number to make X2​ Value 8020​Lower  Limit 00​Target  Result 80024​Upper Limit 79.999999920​ Targel Result 32003200​​

Accepted Answer

A)   80
B)   800
C)   2400
D)   3200 E) B) and C)
F) A) and B)

Question 6

The absolute value of the shadow price indicates the amount by which the objective function will be

Accepted Answer

A)   improved if the corresponding constraint is loosened.
B)   improved if the corresponding constraint is tightened.
C)   made worse if the corresponding constraint is loosened.
D)   improved if the corresponding constraint is unchanged.E) None of the above
F) C) and D)

Question 7

Exhibit 4.2
The following questions correspond to the problem below and associated Risk Solver Platform (RSP) 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:
 -homewark can account far up to $25 \%$ of the grade, but must be at least $5 \%$ af the grade;
- the praject can account for up to $25 \%$ of the grade, but must be at least $5 \%$ af the grade;
- the mid-term and final must each accaunt far betwen $10 \%$ and $40 \%$ of the grade but cannot accaunt far mare than $7 \%$ of the grade when the percentages are cambined; and 
-the project and final exam grades may not collectively constitute more than $50 \%$ of the Iratade. The following LP model allows Robert to maximize his numerical grade.
 $$\begin{array} { l } 
\text { Let } \quad W _ { 1 } = \text { weight as51gMed to hamewark } \
W _ { \mathbf { 2 } } = \text { waight as5igned to the praject } \
W _ { 3 } = \text { weight assigned to the midi-term } \
W _ { 4 } = \text { waight as5igned to the final } \\
\text { MAX: } \quad 75 \mathrm {~W} _ { 1 } + 94 \mathrm {~W} _ { 2 } + 85 \mathrm {~W} _ { 3 } + 92 \mathrm {~W} _ { 4 } \
\text { Subject ta: } \quad W _ { 1 } + W _ { 2 } + W _ { 3 } + W _ { 4 } = 1 \
W _ { 3 } + W _ { 4 } \leq 0.70 \
W _ { 3 } + W _ { 4 } \geq 0.50 \
\text { 0. } 05 \leq W _ { 1 } \leq 0.25 \
\text { 0. } 05 \leq W _ { 2 } \leq 0.25 \
\text { 0.10 } \leq W _ { 3 } \leq 0 .4 0 \
0 .10 \leq W _ { 4 } \leq 0.40 \
\end{array}$$ $\text { Adjustaibla Calls}$

$\begin{array}{llrrrrr}
&&\text { Final } & \text { Reduced } & \text { Objective} & \text {  Allowable } & \text { Allowable }\
\text { Cell } & \text { Name } & \text { Value } & \text { Cost  } & \text {Coefficient  } & \text {Increase } & \text { Decrease }\
\hline \$ F \$ 5 & \text { Mid Term to grade } & 0.40 & 10.00 & 85 & 1 \mathrm{E}+30 & 10 \
\$ F \$ 6 & \text { Final to grade } & 0.25 & 0.00 & 92 & 2 & 17 \
\$ F \$ 7 & \text { Project to grade } & 0.25 & 2.00 & 94 & 1 \mathrm{E}+30 & 2 \
\$ F \$ 8 & \text { Homework to grade } & 0.10 & 0.00 & 75 & 10 & 1 \mathrm{E}+30
\end{array}$

$\text { Constraints }$ 
$\begin{array}{llrrrrrr}
&&\text { Final } & \text { Shadow  } & \text { Constraint} & \text {  Allowable } & \text { Allowable }\
\text { Cell } & \text { Name } & \text { Value } & \text { Price } & \text { R.H. Side } & \text { Increase } & \text { Decrease } \
\hline \$ E \$ 14 & \text { Both Exams Total } & 0.65 & 0 & 0.7 & 1 \mathrm{E}+30 & 0.05 \
\$ E \$ 15 & \text { Final \& Project Total } & 0.5 & 17 & 0.5 & 0.05 & 0.15 \
\$ F \$ 9 & 100 \% \text { to gracle } & 1.00 & 75.00 & 1 & 0.15 & 0.05
\end{array}$
-Refer to Exhibit 4.2. Based on the Risk Solver Platform (RSP) 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

Benefits of sensitivity analysis include all the following except:

Accepted Answer

A)   provides a better picture of how solutions change as model factors change.
B)   fosters managerial acceptance of the optimal solution.
C)   overcomes management skepticism of optimal solutions.
D)   answers potential managerial questions regarding the solution to an LP problem.E) A) and B)
F) B) and C)

Question 9

When automatically running multiple optimizations in Risk Solver Platform (RSP) , what spreadsheet function indicates which optimization is being run?

Accepted Answer

A)   =PsiOptNum() 
B)   =PsiOptValue() 
C)   =PsiOptIndex() 
D)   =PsiCurrentOpt() E) B) and C)
F) C) and D)

Question 10

When a solution is degenerate the shadow prices and their ranges

Accepted Answer

A)   may be interpreted in the usual way but they may not be unique.
B)   must be disregarded.
C)   are always valid and unique.
D)   are always understatedE) A) and B)
F) A) and D)

Question 11

Given the following Risk Solver Platform (RSP) sensitivity output what range of values can the objective function coefficient for variable X1 assume without changing the optimal solution?
 $\text {Changing Calls}$
$\begin{array}{llrrrrr}
&&\text { Final} &\text {Reduced }&\text {Objective }&\text {Allowable}&\text { Allowable }\
\text { Cell } & \text { Name } & \text { Value } & \text { Cost } & \text { Coefficient } & \text { Increase } & \text { Decrease } \
\hline \$ \mathrm{~B} \$ 4 & \text { Number to make: } \mathrm{X} 1 & 9.49 & 0 & 5 & 1.54 & 1 \
\$ \mathrm{C} \$ 4 & \text { Number to make: } \mathrm{X} 2 & 1.74 & 0 & 6 & 1.5 & 1.47
\end{array}$

$\text {Constraints}$
$\begin{array}{llrrrrr}
&&\text { Final } &\text {Shadow} &\text { Constraint } &\text {Allowable} &\text { Allowable }\
\text { Cell } & \text { Name } & \text { Value } & \text { Price } & \text { R.H. Side } & \text { Increase } & \text { Decrease } \
\hline \$ \mathrm{D} \$ 8 & \text { Used } & 42 & 0 & 48 & 1 \mathrm{E}+30 & 6 \
\$ \mathrm{D} \$ 9 & \text { Used } & 132 & 0.24 & 132 & 12 & 12 \
\$ \mathrm{D} \$ 10 & \text { Used } & 24 & 124 & 24 & 133 & 2
\end{array}$

Accepted Answer

The answer of Given the following Risk Solver Platform (RSP)...

Question 12

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.
Suppose the company can purchase more varnishing time for $3.00, should it be purchased and how much can be bought before the value of the additional time is uncertain? 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
 $\text { MAX: } \quad 30 \mathrm{X}_{1}+40 \mathrm{X}_{2}$
$\begin{array}{l}
\text { Subject to: }\
\begin{array} { l } 
6 X _ { 1 } + 4 X _ { 2 } \leq 36 \text { (carpentry) } \
4 X _ { 1 } + \mathbf { 8 } X _ { 2 } \leq 40 \text { (varnishing } \
X _ { 2 } \leq \mathbf { 8 } \left( \text { demand for } X _ { 2 } \right) \
X _ { 1 } , X _ { 2 } \geq 0
\end{array}
\end{array}$ $\text { Changing Cells}$
$\begin{array}{llrrrrr}
&&\text { Final } & \text { Reduced } & \text { Objective } & \text { Allowable } & \text { Allowable }\
\text { Cell } & \text { Name } & \text { Value } & \text { Cost } & \text { Coefficient } & \text { Increase } & \text { Decrease } \
\hline \$ \mathrm{~B} \$ 4 & \text { Number to make: Beds } & 4 & 0 & 30 & 30 & 10 \
\$ \mathrm{C} \$ 4 & \text { Number to make: Desks } & 3 & 0 & 40 & 20 & 20
\end{array}$

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

Accepted Answer

Yes, because the cost of $3.00...

Question 13

Meaningful Risk Solver Platform (RSP)  sensitivity report headings can be defined

Accepted Answer

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

Question 14

The coefficients in an LP model (cj, aij, bj)  represent

Accepted Answer

A)   random variables.
B)   numeric constants.
C)   random constants.
D)   numeric variables.E) A) and D)
F) A) and C)

Question 15

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. The following table summarizes the data for the problem.
 $$\begin{array} { l | c c c c c } 
\text { Crap } & \begin{array} { c } 
\text { Profitper } \
\text { Acre ( }
\end{array} & \begin{array} { c } 
\text { Yied per } \
\text { Acre (lb) }
\end{array} & \begin{array} { c } 
\text { Meximum } \
\text { Denand (lb) }
\end{array} & \begin{array} { c } 
\text { Irripation } \
\text { (acreft) }
\end{array} & \begin{array} { c } 
\text { Fetilize } \
\text { (pounds/are) }
\end{array} \
\hline \text { Carm } & 2,100 & 21,000 & 200,000 & 2 & 500 \
\text { pumplin } & 900 & 10,000 & 180,000 & 3 & 400 \
\text { Beans } & 1,050 & 3,500 & 80,000 & 1 & 300
\end{array}$$ Suppose the farmer can purchase more fertilizer for $2.50 per pound, should he purchase it and how much can he buy and still be sure of the value of the additional fertilizer? Base your response on the following Risk Solver Platform (RSP) sensitivity output.
 $\text { Changing Cells}$
$\begin{array}{llrrrrr}
&&\text { Final } & \text { Reduced } & \text { Objective } & \text { Allowable } & \text { Allowable }\
\text { Cell } & \text { Name } & \text { Value } & \text { Cost } & \text { Coefficient } & \text { Increase } & \text { Decrease } \
\hline \$ B \$ 4 & \text { Acres of Corn } & 9.52 & 0 & 2100 & 1 \mathrm{E}+30 & 350 \
\$ \mathrm{C} \$ 4 & \text { Acres of Pumpkin } & 0 & -500.01 & 899.99 & 500.01 & 1 \mathrm{E}+30 \
\$ \mathrm{D} \$ 4 & \text { Acres of Beans } & 10.79 & 0 & 1050 & 210 & 375.00
\end{array}$

$\text { Constraints }$
$\begin{array}{llrrrrr}
&&\text { Final } & \text {Shadow } & \text {Constraint } & \text {Allowable } & \text {Allowable }\
\text { Cell } & \text { Name } & \text { Value } & \text { Price } & \text { R.H. Side } & \text { Increase } & \text { Decrease } \
\hline \$ \mathrm{E} \$ 8 & \text { Corn demand Used } & 200000 & 0.017 & 200000 & 136000 & 152000 \
\$ \mathrm{E} \$ 9 & \text { Pumpkin demand Used } & 0 & 0 & 180000 & 1 \mathrm{E}+30 & 180000 \
\$ \mathrm{E} \$ 10 & \text { Bean demand Used } & 37777.78 & 0 & 80000 & 1 \mathrm{E}+30 & 42222.22 \
\$ \mathrm{E} \$ 11 & \text { Water Used } & 29.84 & 0 & 50 & 1 \mathrm{E}+30 & 20.15 \
\$ \mathrm{~F} \$ 12 & \text { Fertilizer Userl } & 8000 & 35 & 8000 & 3610 ก 4 & 323800
\end{array}$

Accepted Answer

Yes, because the cost of $2.50...

Question 16

Identify the different sets of basic variables that might be used to obtain a solution to this problem.
 MIN: $\quad 2.5 \mathbf { X } _ { 1 } + 1.5 \mathbf { X } _ { \mathbf { 2 } }$
Subject to:
$$\begin{array} { l } 
4 X _ { 1 } + 3 X _ { 2 } \geq 24 \
2 X _ { 1 } + 4 X _ { 2 } \geq 24 \
X _ { 1 } ,X _ { 2 } \geq 0
\end{array}$$

Accepted Answer

The answer of Identify the different sets of basic variables...

Question 17

The allowable increase for a changing cell (decision variable)  is

Accepted Answer

A)   how many more units to produce to maximize profits.
B)   the amount by which the objective function coefficient can increase without changing the optimal solution.
C)   how much to charge to get the optimal solution.
D)   the amount by which constraint coefficient can increase without changing the optimal solution.E) A) and B)
F) All of the above

Question 18

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.E) All of the above
F) A) and B)

Question 19

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. Of the three percentage of effort constraints, Shipped by Truck, Shipped by Rail, and Shipped by Air, which should be examined for potential cost reduction?

Accepted Answer

The percentage by Truck, Shipp...

Question 20

What is the value of the slack variable in the following constraint when X1 and X2 are nonbasic and only non-negativity is used as simple bounds? X1 + X2 + S1 = 100

Accepted Answer

A)   0
B)   50
C)   100
D)   can't be determined from the given informationE) None of the above
F) A) and D)

Exam 4: Sensitivity Analysis and the Simplex Method

When a solution is degenerate the shadow prices and their ranges

Correct Answer
verified

Correct Answer
verified
Yes, because the cost of $3.00...
View Answer

Correct Answer
verified
The percentage by Truck, Shipp...
View Answer

Meaningful Risk Solver Platform (RSP) sensitivity report headings can be defined

Correct Answer
verified

The allowable increase for a changing cell (decision variable) is

Correct Answer
verified

The absolute value of the shadow price indicates the amount by which the objective function will be

Correct Answer
verified

Correct Answer
verified

The Simplex method uses which of the following values to determine if the objective function value can be improved?

Correct Answer
verified

Why might a decision maker prefer a solution in the interior of the feasible region of a linear programming problem?

Correct Answer
verified

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

Correct Answer
verified

What is the value of the slack variable in the following constraint when X₁ and X₂ are nonbasic and only non-negativity is used as simple bounds? X₁+ X₂ + S₁ = 100

Correct Answer
verified

Risk Solver Platform (RSP) provides sensitivity analysis information on all of the following except the

Correct Answer
verified

Correct Answer
verified

Benefits of sensitivity analysis include all the following except:

Correct Answer
verified

Correct Answer
verified
Yes, because the cost of $2.50...
View Answer

The coefficients in an LP model (c_j, a_ij, b_j) represent

Correct Answer
verified

The slope of the level curve for the objective function value can be changed by

Correct Answer
verified

Correct Answer
verified
Robert can request an increase...
View Answer

When automatically running multiple optimizations in Risk Solver Platform (RSP) , what spreadsheet function indicates which optimization is being run?

Correct Answer
verified

Correct Answer
verified

Exam 4: Sensitivity Analysis and the Simplex Method

When a solution is degenerate the shadow prices and their ranges

Correct AnswerverifiedShow Answer

Correct AnswerverifiedYes, because the cost of $3.00...View AnswerShow Answer

Correct AnswerverifiedThe percentage by Truck, Shipp...View AnswerShow Answer

Meaningful Risk Solver Platform (RSP) sensitivity report headings can be defined

Correct AnswerverifiedShow Answer

The allowable increase for a changing cell (decision variable) is

Correct AnswerverifiedShow Answer

The absolute value of the shadow price indicates the amount by which the objective function will be

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

The Simplex method uses which of the following values to determine if the objective function value can be improved?

Correct AnswerverifiedShow Answer

Why might a decision maker prefer a solution in the interior of the feasible region of a linear programming problem?

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

What is the value of the slack variable in the following constraint when X1 and X2 are nonbasic and only non-negativity is used as simple bounds? X1 + X2 + S1 = 100

Correct AnswerverifiedShow Answer

Risk Solver Platform (RSP) provides sensitivity analysis information on all of the following except the

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Benefits of sensitivity analysis include all the following except:

Correct AnswerverifiedShow Answer

Correct AnswerverifiedYes, because the cost of $2.50...View AnswerShow Answer

The coefficients in an LP model (cj, aij, bj) represent

Correct AnswerverifiedShow Answer

The slope of the level curve for the objective function value can be changed by

Correct AnswerverifiedShow Answer

Correct AnswerverifiedRobert can request an increase...View AnswerShow Answer

When automatically running multiple optimizations in Risk Solver Platform (RSP) , what spreadsheet function indicates which optimization is being run?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct Answer
verified

Correct Answer
verified
Yes, because the cost of $3.00...
View Answer

Correct Answer
verified
The percentage by Truck, Shipp...
View Answer

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

What is the value of the slack variable in the following constraint when X₁ and X₂ are nonbasic and only non-negativity is used as simple bounds? X₁+ X₂ + S₁ = 100

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified
Yes, because the cost of $2.50...
View Answer

The coefficients in an LP model (c_j, a_ij, b_j) represent

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified
Robert can request an increase...
View Answer

Correct Answer
verified

Correct Answer
verified