Question 1

An optimization technique useful for solving problems with more than one objective function is

Accepted Answer

A) dual programming. 
B) sensitivity analysis. 
C) multi-objective linear programming. 
D) goal programming. 
A) dual programming. 
B) sensitivity analysis. 
C) multi-objective linear programming. 
D) goal programming. C

Question 2

What is the meaning of the ti term in this objective function for a goal programming problem?
$\operatorname{MIN} \sum \frac{1}{t_{i}}\left(d_{i}^{-}+d_{i}^{+}\right)^{2}$
$\operatorname{MIN} \sum \frac{1}{t_{i}}\left(d_{i}^{-}+d_{i}^{+}\right)^{2}$

Accepted Answer

A) The time required for each decision variable. 
B) The percent of goal i met. 
C) The coefficient for the ith decision variable 
D) The target value for goal i. 
A) The time required for each decision variable. 
B) The percent of goal i met. 
C) The coefficient for the ith decision variable 
D) The target value for goal i. D

Question 3

Exhibit 7.4
The following questions are based on the problem below.
Robert Gardner runs a small,local-only delivery service.His fleet consists of three smaller panel trucks.He recently accepted a contract to deliver 12 shipping boxes of goods for delivery to 12 different customers.The box weights are: 210,160,320,90,110,70,410,260,170,240,80 and 180 for boxes 1 through 12,respectively.Since each truck differs each truck has different load capacities as given below:
 $\begin{array}{llll}\text { Truck} & \text { Weight Capacity } & \text { Box Capacity } & \text { Cost per pound }\
\hline 1 & 800 \text { pounds } & 5 & \$ 0.34 \
2 & 900 \text { pounds } & 6 & \$ 0.42 \
3 & 700 \text { pounds } & 4 & \$ 0.25
\end{array}$ Robert would like each truck equally loaded,both in terms of number of boxes and in terms of total weight,while minimizing his shipping costs.Assume a cost of $50 per item for trucks carrying extra boxes and $0.10 per pound cost for trucks carrying less weight.
The following integer goal programming formulation applies to his problem.
YS1U1B11 S1U1B0= weight loaded in truck 1;YS1U1B12 S1U1B0= weight loaded in truck 2;YS1U1B13 S1U1B0= weight loaded intruck3;XS1U1B1i,j S1U1B0= 0 if truck i not loaded with box j;1 if truck i loaded with box j.
Given the following spreadsheet solution of this integer goal programming formulation,answer the following questions.
  
-Refer to Exhibit 7.4.The spreadsheet model has scaled all the weights from pounds into 100s pounds.How does this scaling effect the solution obtained using the Risk Solver Platform RSP)?

Accepted Answer

The solution obtained is the same regardless of scaling.In terms of pounds,the total cost would be multiplied by 100,to obtain $78,967.

Question 4

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:
 $\begin{array}{lrrr}&&&\text { Minimum }\
\text { Fund } & \text { Rate of return } & \text { Risk }&\text { investment }\
\hline\mathrm{A} & 12 \% & 0.5 & \$ 20,000 \
\mathrm{~B} & 9 \% & 0.3 & \$ 10.000
\end{array}$ 
Note that a low Risk rating means a less risky investment.The investor can invest to maximize the expected rate of return or minimize risk.Any money beyond the minimum investment requirements can be invested in either fund.
The following is the multi-objective linear programming MOLP)formulation for this problem:
Let X1 = dollars in investment A X2 = dollars in investment B
MAX: 0.12 X1/50000 + 0.09 X2/50000
MIN: 0.5 X1/50000 + 0.3 X2/50000
Subject to: X1 + X2 = 50000
X1 ≥ 20000
X2 ≥ 10000
Xi ≥ 0 for all i
The solution for the second LP is X1,X2)= 20,000,30,000).
Based on this solution,what values should go in cells B2:D11 of the spreadsheet?
 $\begin{array}{|c|l|c|c|c|}
\hline &{\text { A }} & \text { B } & \text { C } & \text { D } \
\hline 1 & \text { Problem data } & \text { A } & \text { B } & \
\hline 2 & \text { Expected return } & & & \
\hline 3 & \text { Risk rating } & & & \
\hline4 & & & & \
\hline 5 & \text { Variables } & \text { A } & \text { B } & \text { Total } \
\hline 6 & \text { Amount invested } & & & \
\hline 7 & \text { Minimum required } & & & \\hline 8 & \
\hline 9 & \text { Objectives: } \
\hline 10 & \text { Average return } \
\hline 11 & \text { Average risk } \
\hline
\end{array}$

Accepted Answer

Question 5

Exhibit 7.4
The following questions are based on the problem below.
Robert Gardner runs a small,local-only delivery service.His fleet consists of three smaller panel trucks.He recently accepted a contract to deliver 12 shipping boxes of goods for delivery to 12 different customers.The box weights are: 210,160,320,90,110,70,410,260,170,240,80 and 180 for boxes 1 through 12,respectively.Since each truck differs each truck has different load capacities as given below:
 $\begin{array}{llll}\text { Truck} & \text { Weight Capacity } & \text { Box Capacity } & \text { Cost per pound }\
\hline 1 & 800 \text { pounds } & 5 & \$ 0.34 \
2 & 900 \text { pounds } & 6 & \$ 0.42 \
3 & 700 \text { pounds } & 4 & \$ 0.25
\end{array}$ Robert would like each truck equally loaded,both in terms of number of boxes and in terms of total weight,while minimizing his shipping costs.Assume a cost of $50 per item for trucks carrying extra boxes and $0.10 per pound cost for trucks carrying less weight.
The following integer goal programming formulation applies to his problem.
YS1U1B11 S1U1B0= weight loaded in truck 1;YS1U1B12 S1U1B0= weight loaded in truck 2;YS1U1B13 S1U1B0= weight loaded intruck3;XS1U1B1i,j S1U1B0= 0 if truck i not loaded with box j;1 if truck i loaded with box j.
Given the following spreadsheet solution of this integer goal programming formulation,answer the following questions.
  
-Refer to Exhibit 7.4.The solution indicates Truck 3 is under the target weight by 67 pounds.What if anything can be done to this model to provide a solution in which Truck 3 is closer to the target weight?

Accepted Answer

Nothing.Tr

Question 6

Deviational variables

Accepted Answer

A) are added to constraints to indicate acceptable departures from the target vaoues of their corresponding goals 
B) are negative 
C) are positive for underachievement only 
D) are positive for overachievement only 
A) are added to constraints to indicate acceptable departures from the target vaoues of their corresponding goals 
B) are negative 
C) are positive for underachievement only 
D) are positive for overachievement only

Question 7

If no other feasible solution to a multi-objective linear programming MOLP)problem allows an increase in any objective without decreasing at least one other objective,the solution is said to be

Accepted Answer

A) dually optimal. 
B) Pareto optimal. 
C) suboptimal. 
D) maximally optimal. 
A) dually optimal. 
B) Pareto optimal. 
C) suboptimal. 
D) maximally optimal.

Question 8

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+,the following constraint can be used to express this goal.
3 X1 + 4 X2 + d1? ? d1+  = 36
If we obtain a solution where X1 = 6 and X2 = 2,what values do the deviational variables assume?

Accepted Answer

A) $\mathrm{d}_{1}^{-}=0, \mathrm{~d}_{1}^{+}=10$ 
B) $\mathrm{d}_{1}^{-}=10, \mathrm{~d}_{1}^{+}=0$ 
C) $\mathrm{d}_{1}^{-}=5, \mathrm{~d}_{1}^{+}=5$ 
D) $\mathrm{d}_{1}^{-}=6, \mathrm{~d}_{1}^{+}=0$ 
A) $\mathrm{d}_{1}^{-}=0, \mathrm{~d}_{1}^{+}=10$ 
B) $\mathrm{d}_{1}^{-}=10, \mathrm{~d}_{1}^{+}=0$ 
C) $\mathrm{d}_{1}^{-}=5, \mathrm{~d}_{1}^{+}=5$ 
D) $\mathrm{d}_{1}^{-}=6, \mathrm{~d}_{1}^{+}=0$

Question 9

A company makes 2 products A and B from 2 resources,labor and material.The products have the following resource requirements and produce the accompanying profits.The available quantity of resources is also shown in the table.
 $$\begin{array} { l r r c } 
\text { Praduct } & \text { A } & \text { B } & \text { Available resources } \
\hline \text { Labor hr/unit) } & 3 & 2 & 150 \
\text { Material ounces/unit) } & 1 & 2 & 200\
\text { Profit\$/unit)}&7&6
\end{array}$$ 
Management has developed the following set of goals
Goal 1: Produce approximately 40 units of product 1.
Goal 2: Produce approximately 70 units of product 2.Goal 3: Achieve a profit over $400.
Goal 4: Consume less than 150 hours of labor Goal 5: Consume less than 200 ounces of material
Formulate a goal programming model of this problem.

Accepted Answer

The answer of A company makes 2 products A and...

Question 10

The "triple bottom line" incorporates multiple objective decision-making by:

Accepted Answer

A) simultaneously considering profit,people and planet 
B) environmental issues only 
C) financial objectives only 
D) wealth redistribution in the society 
A) simultaneously considering profit,people and planet 
B) environmental issues only 
C) financial objectives only 
D) wealth redistribution in the society

Question 11

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)isare)the target 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 12

Decision-making problems which can be stated as a collection of desired objectives are known as what type of problem?

Accepted Answer

A) A non-linear programming problem. 
B) An unconstrained programming problem. 
C) A goal programming problem. 
D) An integer programming problem. 
A) A non-linear programming problem. 
B) An unconstrained programming problem. 
C) A goal programming problem. 
D) An integer programming problem.

Question 13

Goal programming GP)is typically

Accepted Answer

A) a minimization problem of the sum of weighted percentage deviations 
B) a maximization problem of positive deviations only 
C) a minimization problem of negative deviations only 
D) a maximization problem of continuous goals 
A) a minimization problem of the sum of weighted percentage deviations 
B) a maximization problem of positive deviations only 
C) a minimization problem of negative deviations only 
D) a maximization problem of continuous goals

Question 14

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:
 $\begin{array}{lrrr}&&&\text { Minimum }\
\text { Fund } & \text { Rate of return } & \text { Risk }&\text { investment }\
\hline\mathrm{A} & 12 \% & 0.5 & \$ 20,000 \
\mathrm{~B} & 9 \% & 0.3 & \$ 10.000
\end{array}$ 
Note that a low Risk rating means a less risky investment.The investor can invest to maximize the expected rate of return or minimize risk.Any money beyond the minimum investment requirements can be invested in either fund.
The following is the MOLP formulation for this problem:

The solution for the second LP is X1,X2)= 20,000,30,000).
What formulas should go in cells B2:D11 of the spreadsheet? NOTE: Formulas are not required in all of these cells.
 $\begin{array}{|c|c|c|c|c|}
\hline & \text { A } & \text { B } & \text { C } & \text { D } \
\hline 1 & \text { Problem data } & \text { A } & \text { B } & \
\hline 2 & \text { Expected return } & 12 \% & 9 \% & \
\hline 3 & \text { Risk rating } & 0.50 & 0.20 & \\hline 4\\hline 5 & \text { Variables } & \text { A } & \text { B } & \text { Total } \
\hline 6 & \text { Amount invested } & \$ 20,000 & \$ 30,000 & \$ 50,000 \
\hline 7 & \text { Minimum required } & \$ 20,000 & \$ 10,000 & \$ 50,000 \
\hline 8 & & & & \\hline 9 & \text { Objectives: } & \
\hline 10 & \text { Average return } & 10.2 \% \
\hline 11 & \text { Average risk } & 0.32 \
\hline
\end{array}$

Accepted Answer

Cell Formula
 @#IMG-DLM&
 D6 =

Question 15

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.What formula goes in cell B9?

Accepted Answer

A) =SUMB6:B8) 
B) =B6+B7-B8 
C) =B6-B7+B8 
D) =B10-B8 
A) =SUMB6:B8) 
B) =B6+B7-B8 
C) =B6-B7+B8 
D) =B10-B8

Question 16

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:
 $\begin{array}{lrrr}&&&\text { Minimum }\
\text { Fund } & \text { Rate of return } & \text { Risk }&\text { investment }\
\hline\mathrm{A} & 12 \% & 0.5 & \$ 20,000 \
\mathrm{~B} & 9 \% & 0.3 & \$ 10.000
\end{array}$ 
Note that a low Risk rating means a less risky investment.The investor can invest to maximize the expected rate of return or minimize risk.Any money beyond the minimum investment requirements can be invested in either fund.
Formulate the MOLP for this investor.

Accepted Answer

The answer of An investor wants to invest $50,000 in...

Question 17

Consider the following multi-objective linear programming problem MOLP):
MAX: 3 X1 + 4 X2
MAX: 2 X1 + X2
Subject to: 6 X1 + 13 X2 ? 78
12 X1 + 9 X2 ? 108
8 X1 + 10 X2 ? 80 X1,X2 ? 0
Graph the feasible region for this problem and compute the value of each objective at each extreme point.What are the solutions to each of the component LPs?

Accepted Answer

@#IMG-DLM& \[\begin{array} { l l l l } 
\mathbf {

Question 18

The RHS value of a goal constraint is referred to as the

Accepted Answer

A) target value. 
B) constraint value. 
C) objective value. 
D) desired value. 
A) target value. 
B) constraint value. 
C) objective value. 
D) desired value.

Question 19

Suppose that X1 equals 4.What are the values for d1+ and d1? in the following constraint?
X1 + d1?? d1+  = 8

Accepted Answer

A) $\mathrm{d}_{1}^{-}=4, \mathrm{~d}_{1}^{+}=0$ 
B) $\mathrm{d}_{1}^{-}=0, \mathrm{~d}_{1}^{+}=4$ 
C) $\mathrm{d}_{1}^{-}=4, \mathrm{~d}_{1}^{+}=4$ 
D) $\mathrm{d}_{1}^{-}=8, \mathrm{~d}_{1}^{+}=0$ 
A) $\mathrm{d}_{1}^{-}=4, \mathrm{~d}_{1}^{+}=0$ 
B) $\mathrm{d}_{1}^{-}=0, \mathrm{~d}_{1}^{+}=4$ 
C) $\mathrm{d}_{1}^{-}=4, \mathrm{~d}_{1}^{+}=4$ 
D) $\mathrm{d}_{1}^{-}=8, \mathrm{~d}_{1}^{+}=0$

Question 20

In the "triple bottom line" the term "people" refers to:

Accepted Answer

A) social responsibility issues 
B) environmental issues 
C) financial objectives 
D) all of the above 
A) social responsibility issues 
B) environmental issues 
C) financial objectives 
D) all of the above

An optimization technique useful for solving problems with more than one objective function is

What is the meaning of the t_iterm in this objective function for a goal programming problem? $\operatorname{MIN} \sum \frac{1}{t_{i}}\left(d_{i}^{-}+d_{i}^{+}\right)^{2}$ $\operatorname{MIN} \sum \frac{1}{t_{i}}\left(d_{i}^{-}+d_{i}^{+}\right)^{2}$

Deviational variables

If no other feasible solution to a multi-objective linear programming MOLP)problem allows an increase in any objective without decreasing at least one other objective,the solution is said to be

The "triple bottom line" incorporates multiple objective decision-making by:

Decision-making problems which can be stated as a collection of desired objectives are known as what type of problem?

Goal programming GP)is typically

The RHS value of a goal constraint is referred to as the

Suppose that X₁equals 4.What are the values for d₁⁺ and d₁^?in the following constraint? X₁ + d₁^?? d₁⁺ = 8

In the "triple bottom line" the term "people" refers to:

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

An optimization technique useful for solving problems with more than one objective function is

Deviational variables

If no other feasible solution to a multi-objective linear programming MOLP)problem allows an increase in any objective without decreasing at least one other objective,the solution is said to be

The "triple bottom line" incorporates multiple objective decision-making by:

Decision-making problems which can be stated as a collection of desired objectives are known as what type of problem?

Goal programming GP)is typically

The RHS value of a goal constraint is referred to as the

Suppose that X1 equals 4.What are the values for d1+ and d1? in the following constraint? X1 + d1?? d1+ = 8

In the "triple bottom line" the term "people" refers to:

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 X₁equals 4.What are the values for d₁⁺ and d₁^?in the following constraint? X₁ + d₁^?? d₁⁺ = 8