Question 1

The primary benefit of a MINIMAX objective function is

Accepted Answer

A) it yields any feasible solution by changing the weights. 
B) it is limited to all corner points. 
C) it yields a larger variety of solutions than generally available using an LP method. 
D) it makes many of the deviational variables equal to zero. 
A) it yields any feasible solution by changing the weights. 
B) it is limited to all corner points. 
C) it yields a larger variety of solutions than generally available using an LP method. 
D) it makes many of the deviational variables equal to zero.

Question 2

Suppose that the first goal in a GP problem is to make 3 X1 + 4 X2 approximately equal to 36.Using the deviational variables d1? and d1+,what constraint can be used to express this goal?

Accepted Answer

A) $3 \mathrm{X}_{1}+4 \mathrm{X}_{2}+\mathrm{d}_{1}^{-}-\mathrm{d}_{1}^{+} \leq 36$ 
B) $3 \mathrm{x}_{1}+4 \mathrm{X}_{2}-\mathrm{d}_{1}^{-}-\mathrm{d}_{1}^{+}=36$ 
C) $3 \mathrm{X}_{1}+4 \mathrm{X}_{2}+\mathrm{d}_{1}^{-}+\mathrm{d}_{1}^{+}=30$ 
D) $3 \mathrm{X}_{1}+4 \mathrm{X}_{2}+\mathrm{d}_{1}^{--} \mathrm{d}_{1}^{+}=36$ 
A) $3 \mathrm{X}_{1}+4 \mathrm{X}_{2}+\mathrm{d}_{1}^{-}-\mathrm{d}_{1}^{+} \leq 36$ 
B) $3 \mathrm{x}_{1}+4 \mathrm{X}_{2}-\mathrm{d}_{1}^{-}-\mathrm{d}_{1}^{+}=36$ 
C) $3 \mathrm{X}_{1}+4 \mathrm{X}_{2}+\mathrm{d}_{1}^{-}+\mathrm{d}_{1}^{+}=30$ 
D) $3 \mathrm{X}_{1}+4 \mathrm{X}_{2}+\mathrm{d}_{1}^{--} \mathrm{d}_{1}^{+}=36$

Question 3

Goal programming solution feedback indicates that the d4+ level of 50 should not be exceeded in future solution iterations.How should you modify your goal constraint to accommodate this requirement?
40 X1 + 20 X2 + d4? + d4+ = 300

Accepted Answer

A) $\text { Increase the RHS value from } 300 \text { to } 350 \text {. }$ 
B) $\text { Replace the constraint with } 40 \mathrm{X}_{1}+20 \mathrm{X}_{2} \leq 350$ 
C) $\text { Do not modify the constraint, add a constraint } \mathrm{d}_{4}^{+} \leq 50$ 
D) $\text { Do not modify the constraint, add a constraint } d_{4}+=50$ 
A) $\text { Increase the RHS value from } 300 \text { to } 350 \text {. }$ 
B) $\text { Replace the constraint with } 40 \mathrm{X}_{1}+20 \mathrm{X}_{2} \leq 350$ 
C) $\text { Do not modify the constraint, add a constraint } \mathrm{d}_{4}^{+} \leq 50$ 
D) $\text { Do not modify the constraint, add a constraint } d_{4}+=50$

Question 4

A constraint which cannot be violated is called a

Accepted Answer

A) binding constraint. 
B) hard constraint. 
C) definite constraint. 
D) required constraint. 
A) binding constraint. 
B) hard constraint. 
C) definite constraint. 
D) required constraint.

Question 5

Exhibit 7.2
The following questions are based on the problem below.
An investor has $150,000 to invest in investments A and B.Investment A requires a $10,000 minimum investment,pays a return of 12% and has a risk factor of .50.Investment B requires a $15,000 minimum investment,pays a return of 10% and has a risk factor of .20.The investor wants to maximize the return while minimizing the risk of the portfolio.The following multi-objective linear programming MOLP)has been solved in Excel.
 $\begin{array}{|c|l|c|c|c|} 
\hline& {\text { A }} & \text { B } & \text { C } & \text { D } \
\hline 1 & \text { Problem data } & \text { A } & \text { B } & \
\hline 2 & \text { Expected return } & 12 \% & 10 \% & \
\hline 3 & \text { Risk rating } & 0.50 & 0.20 & \\hline 4 & & & & \
\hline 5 & \text { Variables } & \mathrm{A} & \mathrm{B} & \text { Total } \
\hline 6 & \text { Amount invested } & 0 & 0 & 0 \
\hline 7 & \text { Minimum required } & \$ 10,000 & \$ 15,000 & \$ 150,000 \\hline 8 & & \
\hline 9 & \text { Objectives: } & \
\hline 10 & \text { Average return } & 0 \
\hline 11 & \text { Average risk } & 0 \
\hline
\end{array}$
-Refer to Exhibit 7.2.What formula goes in cell B11?

Accepted Answer

A) =SUMPRODUCTB2:C2,$B$6:$C$6)/$D$7 
B) =B2*C2+B3*C3 
C) =SUMPRODUCTB3:C3,$B$6:$C$6)/$D$7 
D) =SUMPRODUCTB3:C3,$B$6:$C$6) 
A) =SUMPRODUCTB2:C2,$B$6:$C$6)/$D$7 
B) =B2*C2+B3*C3 
C) =SUMPRODUCTB3:C3,$B$6:$C$6)/$D$7 
D) =SUMPRODUCTB3:C3,$B$6:$C$6)

Question 6

Which of the following is true regarding goal programming?

Accepted Answer

A) The objective function is not useful when comparing goal programming solutions. 
B) We can place upper bounds on any of the deviation variables. 
C) A preemptive goal program involves deviations with arbitrarily large weights. 
D) All of these are true. 
A) The objective function is not useful when comparing goal programming solutions. 
B) We can place upper bounds on any of the deviation variables. 
C) A preemptive goal program involves deviations with arbitrarily large weights. 
D) All of these are true.

Question 7

Which of the following are true regarding weights assigned to deviational variables?

Accepted Answer

A) The weights assigned can be negative. 
B) The weights assigned must sum to one. 
C) The weight assigned to the deviation under a particular goal must be the same as the weight assigned to the deviation above that particular goal. 
D) All of these are false. 
A) The weights assigned can be negative. 
B) The weights assigned must sum to one. 
C) The weight assigned to the deviation under a particular goal must be the same as the weight assigned to the deviation above that particular goal. 
D) All of these are false.

Question 8

What weight would be assigned to a neutral deviational variable?

Accepted Answer

A) 0 
B) 1 
C) 10 
D) 100 
A) 0 
B) 1 
C) 10 
D) 100

Question 9

Exhibit 7.1
The following questions are based on the problem below.
A company wants to advertise on TV and radio.The company wants to produce about 6 TV ads and 12 radio ads.Each TV ad costs $20,000 and is viewed by 10 million people.Radio ads cost $10,000 and are heard by 7 million people.The company wants to reach about 140 million people,and spend about $200,000 for all the ads.The problem has been set up in the following Excel spreadsheet.
 $\begin{array}{|c|l|c|c|c|c|} 
\hline&{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } \
\hline 1 & \text { Problem Data } & \text { TV } & \text { Radio } & & \
\hline 2 & \text { Cost } & 20 & 10 & & \
\hline 3 & \text { Coverage } & 10 & 7 & & \
\hline 4 & & & & & \\hline 5 & \text { Goal Constraints } & \text { TV } & \text { Radio } & \text { Cost } & \text { Coverage } \
\hline 6 & \text { Actual Amount } & 0 & 0 & & \
\hline 7 & \text { +Under } & 0 & 0 & 0 & 0 \
\hline 8 & \text { - Over } & 0 & 0 & 0 & 0 \
\hline 9 & \text { F Goal } & 0 & 0 & 0 & 0 \
\hline 10 & \text { Target Value } & 6 & 12 & 200 & 140 \\hline 11 & & & & & \
\hline 12 & \text { Percentage Deviation: } & & & & \
\hline 13 & \text { Under } & 1 & 1 & 1 & 1 \
\hline 14 & \text { Over } & 0 & 0 & 0 & 0 \\hline 15 & & \
\hline 16 & \text { Weights } & \
\hline 17 & \text { Under } & \
\hline 18 & \text { Over } & \
\hline 19 & & \
\hline 20 & \text { Objective } & 0 \
\hline
\end{array}$
-Refer to Exhibit 7.1.Which cells)isare)the objective cells)in this model?

Accepted Answer

A) $B$20 
B) $D$6 
C) $E$6 
D) $B$13:$E$14,$B$9:$E$9 
A) $B$20 
B) $D$6 
C) $E$6 
D) $B$13:$E$14,$B$9:$E$9

Question 10

What is the soft constraint form of the following hard constraint?
3X1 + 2 X2 ? 10

Accepted Answer

A) $3 \mathrm{X}_{1}+2 \mathrm{X}_{2}+\mathrm{d}_{1}^{-}-\mathrm{d}_{1}^{+}=10$ 
B) $3 \mathrm{X}_{1}+2 \mathrm{X}_{2}+\mathrm{d}_{1}+\mathrm{d}_{1}^{+}=10$ 
C) $3 \mathrm{X}_{1}+2 \mathrm{X}_{2}-\mathrm{d}_{1}^{-}-\mathrm{d}_{1}^{+} \leq 10$ 
D) $3 \mathrm{X}_{1}+2 \mathrm{X}_{2}+\mathrm{d}_{1}^{-}-\mathrm{d}_{1}^{+} \geq 10$ 
A) $3 \mathrm{X}_{1}+2 \mathrm{X}_{2}+\mathrm{d}_{1}^{-}-\mathrm{d}_{1}^{+}=10$ 
B) $3 \mathrm{X}_{1}+2 \mathrm{X}_{2}+\mathrm{d}_{1}+\mathrm{d}_{1}^{+}=10$ 
C) $3 \mathrm{X}_{1}+2 \mathrm{X}_{2}-\mathrm{d}_{1}^{-}-\mathrm{d}_{1}^{+} \leq 10$ 
D) $3 \mathrm{X}_{1}+2 \mathrm{X}_{2}+\mathrm{d}_{1}^{-}-\mathrm{d}_{1}^{+} \geq 10$

Question 11

Given the following goal constraints
5 X1 + 6 X2 + 7 X3 + d1− − d1+ = 87
3 X1 + X2 + 4 X3 + d2− − d2+ = 37
7 X1 + 3 X2 + 2 X3 + d3− − d3+ = 72
and solution X1,X2,X3)= 7,2,5),what values do the deviational variables assume?

Accepted Answer

d₁⁻ = 5,d₂⁺ =

Question 12

The di+,di− variables are referred to as

Accepted Answer

A) objective variables. 
B) goal variables. 
C) target variables. 
D) deviational variables. 
A) objective variables. 
B) goal variables. 
C) target variables. 
D) deviational variables.

Question 13

Which of the following is false regarding a goal constraint?

Accepted Answer

A) A goal constraint allows us to determine how close a given solution comes to achieving a goal. 
B) A goal constraint will always contain two deviational variables. 
C) Deviation variables are non-negative. 
D) If two deviation variables are used in a constraint at least one will have a value of zero. 
A) A goal constraint allows us to determine how close a given solution comes to achieving a goal. 
B) A goal constraint will always contain two deviational variables. 
C) Deviation variables are non-negative. 
D) If two deviation variables are used in a constraint at least one will have a value of zero.

Question 14

Exhibit 7.2
The following questions are based on the problem below.
An investor has $150,000 to invest in investments A and B.Investment A requires a $10,000 minimum investment,pays a return of 12% and has a risk factor of .50.Investment B requires a $15,000 minimum investment,pays a return of 10% and has a risk factor of .20.The investor wants to maximize the return while minimizing the risk of the portfolio.The following multi-objective linear programming MOLP)has been solved in Excel.
 $\begin{array}{|c|l|c|c|c|} 
\hline& {\text { A }} & \text { B } & \text { C } & \text { D } \
\hline 1 & \text { Problem data } & \text { A } & \text { B } & \
\hline 2 & \text { Expected return } & 12 \% & 10 \% & \
\hline 3 & \text { Risk rating } & 0.50 & 0.20 & \\hline 4 & & & & \
\hline 5 & \text { Variables } & \mathrm{A} & \mathrm{B} & \text { Total } \
\hline 6 & \text { Amount invested } & 0 & 0 & 0 \
\hline 7 & \text { Minimum required } & \$ 10,000 & \$ 15,000 & \$ 150,000 \\hline 8 & & \
\hline 9 & \text { Objectives: } & \
\hline 10 & \text { Average return } & 0 \
\hline 11 & \text { Average risk } & 0 \
\hline
\end{array}$
-Refer to Exhibit 7.2.What formula goes in cell B10?

Accepted Answer

A) =SUMPRODUCTB2:C2,$B$6:$C$6)/$D$7 
B) =B2*C2+B3*C3 
C) =SUMPRODUCTB3:C3,$B$6:$C$6)/$D$7 
D) =SUMPRODUCTB2:C2,$B$6:$C$6) 
A) =SUMPRODUCTB2:C2,$B$6:$C$6)/$D$7 
B) =B2*C2+B3*C3 
C) =SUMPRODUCTB3:C3,$B$6:$C$6)/$D$7 
D) =SUMPRODUCTB2:C2,$B$6:$C$6)

Question 15

A MINIMAX objective function in goal programming GP):

Accepted Answer

A) is used to minimize the maximum deviation from a goal 
B) is captured in a decision table 
C) is estimated by trial-and-error 
D) often produces an infeasible solution 
A) is used to minimize the maximum deviation from a goal 
B) is captured in a decision table 
C) is estimated by trial-and-error 
D) often produces an infeasible solution

Question 16

A manager wants to ensure that he does not exceed his budget by more than $1000 in a goal programming problem.If the budget constraint is the third constraint in the goal programming problem which of the following formulas will best ensure that the manager's objective is met?

Accepted Answer

A) $\text { MIN } d_{3}^{+}$ 
B) $\mathrm{d}_{3}^{-} \geq 1000$ 
C) $\mathrm{d}_{3}{ }^{+}=1000$ 
D) $\mathrm{d}_{3}{ }^{+} \leq 1000$ 
A) $\text { MIN } d_{3}^{+}$ 
B) $\mathrm{d}_{3}^{-} \geq 1000$ 
C) $\mathrm{d}_{3}{ }^{+}=1000$ 
D) $\mathrm{d}_{3}{ }^{+} \leq 1000$

Question 17

An investor wants to invest $50,000 in two mutual funds,A and B.The rates of return,risks and minimum investment requirements for each fund are:
 $\begin{array}{lll}\text { Fund }&\text { Rate of return }&\text { Risk }&\text { Minimum investment }\
\hline \text { A } & 12 \% & 0.5&\$20,000 \
\text { B } & 9 \% & 0.3&\$10,000
\end{array}$ 
Note that a low Risk rating means a less risky investment.The investor wants to maximize the expected rate of return while minimizing his risk.Any money beyond the minimum investment requirements can be invested in either fund.The investor has found that the maximum possible expected rate of return is 11.4% and the minimum possible risk is 0.32.
The following Excel spreadsheet has been created to solve a goal programming problem with a MINIMAX objective based on the following goal programming formulation with MINIMAX objective and corresponding solution.
MINIMIZE Q
Subject to: X1 + X2 = 50000
X1 ≥ 20000
X2 ≥ 10000
 $w _ { 2 } \left( \frac { \left( \frac { 0.5 X _ { 1 } + 0.3 X _ { 2 } } { 50000 } \right) - 0.32 } { 0.32 } \right) \leq Q$ 
 $w _ { \mathrm { i } } \left( \frac { \left( 0.114 - \frac { 0.12 X _ { 1 } + 0.09 X _ { 2 } } { 50000 } \right) } { 0.114 } \right) \leq Q$ 
 $w_{\mathrm{i}}\left(\frac{\left(0.114-\frac{0.12 X_{1}+0.09 X_{2}}{50000}\right)}{0.114}\right) \leq Q$ 
 $w_{2}\left(\frac{\left(\frac{0.5 x_{i}+0.3 X_{2}}{50000}\right)-0.32}{0.32}\right) \leq Q$ 
Xi ≥ 0 for all i,Q ≥ 0
with solution X1,X2)= 15,370,34,630).
What values should go in cells B2:D14 of the spreadsheet?
 $\begin{array}{|c|l|c|c|c|c|}
\hline &{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } \
\hline 1 & \text { Problem data } & \text { A } & \text { B } & & \
\hline 2 & \text { Expected retum } & & & & \
\hline 3 & \text { Risk rating } & & & & \\hline 4 & & & & \
\hline 5 & \text { Variables } & \text { A } & \text { B } & \text { Total } \
\hline 6 & \text { Amount invested } & & & \
\hline 7 & \text { Minimum required } & & & \
\hline 8 & & & & \\hline 9 & & & & & \text { Weighted } \
\hline 10 & \text { Goals } & \text { Actual } & \text { Target } & \text { Weights } & \% \text { Deviation } \
\hline 11 & \text { Average return } & & & 1 & \
\hline 12 & \text { Average risk } & & & 1 & \
\hline 13 & & & & & \
\hline 14 & \text { Objective: } & & & &\
\hline
\end{array}$

Accepted Answer

Question 18

Goal programming differs from linear programming or integer linear programming is that

Accepted Answer

A) goal programming provides for multiple objectives. 
B) goal programming excludes hard constraints. 
C) with goal programming we iterate until an acceptable solution is obtained. 
D) goal programming requires fewer variables. 
A) goal programming provides for multiple objectives. 
B) goal programming excludes hard constraints. 
C) with goal programming we iterate until an acceptable solution is obtained. 
D) goal programming requires fewer variables.

Question 19

Exhibit 7.2
The following questions are based on the problem below.
An investor has $150,000 to invest in investments A and B.Investment A requires a $10,000 minimum investment,pays a return of 12% and has a risk factor of .50.Investment B requires a $15,000 minimum investment,pays a return of 10% and has a risk factor of .20.The investor wants to maximize the return while minimizing the risk of the portfolio.The following multi-objective linear programming MOLP)has been solved in Excel.
 $\begin{array}{|c|l|c|c|c|} 
\hline& {\text { A }} & \text { B } & \text { C } & \text { D } \
\hline 1 & \text { Problem data } & \text { A } & \text { B } & \
\hline 2 & \text { Expected return } & 12 \% & 10 \% & \
\hline 3 & \text { Risk rating } & 0.50 & 0.20 & \\hline 4 & & & & \
\hline 5 & \text { Variables } & \mathrm{A} & \mathrm{B} & \text { Total } \
\hline 6 & \text { Amount invested } & 0 & 0 & 0 \
\hline 7 & \text { Minimum required } & \$ 10,000 & \$ 15,000 & \$ 150,000 \\hline 8 & & \
\hline 9 & \text { Objectives: } & \
\hline 10 & \text { Average return } & 0 \
\hline 11 & \text { Average risk } & 0 \
\hline
\end{array}$
-Refer to Exhibit 7.2.Which cells are the changing cells in this model?

Accepted Answer

A) $B$6:$C$6,$B$10:$B$11 
B) $B$6:$C$6 
C) $B$6:$D$6 
D) $B$10:$B$11 
A) $B$6:$C$6,$B$10:$B$11 
B) $B$6:$C$6 
C) $B$6:$D$6 
D) $B$10:$B$11

Question 20

The d+
Variable indicates the amount by which each goal's target value is

Accepted Answer

A) missed. 
B) underachieved. 
C) overachieved. 
D) overstated. 
A) missed. 
B) underachieved. 
C) overachieved. 
D) overstated.

The primary benefit of a MINIMAX objective function is

Suppose that the first goal in a GP problem is to make 3 X₁ + 4 X₂ approximately equal to 36.Using the deviational variables d₁^? and d₁⁺,what constraint can be used to express this goal?

Goal programming solution feedback indicates that the d₄⁺level of 50 should not be exceeded in future solution iterations.How should you modify your goal constraint to accommodate this requirement? 40 X₁+ 20 X₂ + d₄^? + d₄⁺ = 300

A constraint which cannot be violated is called a

Which of the following is true regarding goal programming?

Which of the following are true regarding weights assigned to deviational variables?

What weight would be assigned to a neutral deviational variable?

What is the soft constraint form of the following hard constraint? 3X₁+ 2 X₂? 10

Given the following goal constraints 5 X₁ + 6 X₂ + 7 X₃ + d₁⁻ − d₁⁺ = 87 3 X₁ + X₂ + 4 X₃ + d₂⁻ − d₂⁺ = 37 7 X₁ + 3 X₂ + 2 X₃ + d₃⁻ − d₃⁺ = 72 and solution X₁,X₂,X₃)= 7,2,5),what values do the deviational variables assume?

The d_i⁺,d_i⁻ variables are referred to as

Which of the following is false regarding a goal constraint?

A MINIMAX objective function in goal programming GP):

A manager wants to ensure that he does not exceed his budget by more than $1000 in a goal programming problem.If the budget constraint is the third constraint in the goal programming problem which of the following formulas will best ensure that the manager's objective is met?

Goal programming differs from linear programming or integer linear programming is that

The d⁺ Variable indicates the amount by which each goal's target value is

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Sensitivity Analysis and the Simplex Method

Network Modeling

Integer Linear Programming

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 7: Goal Programming and Multiple Objective Optimization

The primary benefit of a MINIMAX objective function is

Suppose that the first goal in a GP problem is to make 3 X1 + 4 X2 approximately equal to 36.Using the deviational variables d1? and d1+,what constraint can be used to express this goal?

Goal programming solution feedback indicates that the d4+ level of 50 should not be exceeded in future solution iterations.How should you modify your goal constraint to accommodate this requirement? 40 X1 + 20 X2 + d4? + d4+ = 300

A constraint which cannot be violated is called a

Which of the following is true regarding goal programming?

Which of the following are true regarding weights assigned to deviational variables?

What weight would be assigned to a neutral deviational variable?

What is the soft constraint form of the following hard constraint? 3X1 + 2 X2 ? 10

Given the following goal constraints 5 X1 + 6 X2 + 7 X3 + d1− − d1+ = 87 3 X1 + X2 + 4 X3 + d2− − d2+ = 37 7 X1 + 3 X2 + 2 X3 + d3− − d3+ = 72 and solution X1,X2,X3)= 7,2,5),what values do the deviational variables assume?

The di+,di− variables are referred to as

Which of the following is false regarding a goal constraint?

A MINIMAX objective function in goal programming GP):

A manager wants to ensure that he does not exceed his budget by more than $1000 in a goal programming problem.If the budget constraint is the third constraint in the goal programming problem which of the following formulas will best ensure that the manager's objective is met?

Goal programming differs from linear programming or integer linear programming is that

The d+ Variable indicates the amount by which each goal's target value is

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Sensitivity Analysis and the Simplex Method

Network Modeling

Integer Linear Programming

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

Suppose that the first goal in a GP problem is to make 3 X₁ + 4 X₂ approximately equal to 36.Using the deviational variables d₁^? and d₁⁺,what constraint can be used to express this goal?

Goal programming solution feedback indicates that the d₄⁺level of 50 should not be exceeded in future solution iterations.How should you modify your goal constraint to accommodate this requirement? 40 X₁+ 20 X₂ + d₄^? + d₄⁺ = 300

What is the soft constraint form of the following hard constraint? 3X₁+ 2 X₂? 10

Given the following goal constraints 5 X₁ + 6 X₂ + 7 X₃ + d₁⁻ − d₁⁺ = 87 3 X₁ + X₂ + 4 X₃ + d₂⁻ − d₂⁺ = 37 7 X₁ + 3 X₂ + 2 X₃ + d₃⁻ − d₃⁺ = 72 and solution X₁,X₂,X₃)= 7,2,5),what values do the deviational variables assume?

The d_i⁺,d_i⁻ variables are referred to as

The d⁺ Variable indicates the amount by which each goal's target value is