Question 1

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

Accepted Answer

A)  d1- = 4, d1+  = 0 
B)  d1- = 0, d1+  = 4 
C)  d1-= 4, d1+  = 4 
D)  d1- = 8, d1+  = 0 
A)  d1- = 4, d1+  = 0 
B)  d1- = 0, d1+  = 4 
C)  d1-= 4, d1+  = 4 
D)  d1- = 8, d1+  = 0 A

Question 2

The di+ 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. C

Question 3

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.
 $$\begin{array} { | c | l | c | c | c | } 
\hline & { \text { A } } & \mathrm { B } & \mathrm { C } & \mathrm { D } \
\hline 1 & \text { Problem data } & \mathrm { A } & \mathrm { B } & \
\hline 2 & \text { Expected retun } & 12 \% & 10 \% & \
\hline 3 & \text { Risk rating } & 0.50 & 0.20 & \
\hline 4 & & & & \
\hline 5 & \text { Variables } & \mathrm { A } & \mathrm { B } & \text { Tatal } \
\hline 6 & \text { Amount invested } & 0 & 0 & 0 \
\hline 7 & \text { Minimum required } & \$ 10,000 & \$ 15,000 & \$ 150,000 \
\hline 8 & & & & \
\hline 9 & \text { Objectives: } & & & \
\hline 10 & \text { Average return } & 0 & & \
\hline 11 & \text { Average risk } & 0 & & \
\hline
\end{array}$$
-Refer to Exhibit 7.2. What formula goes in cell B10?

Accepted Answer

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

Question 4

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:
 $$\begin{array} { c c c c } 
\text { Truck } & \text { Weight Capacity } & \text { Box Capacity } & \text { Cast per pound } \
\hline 1 & \text { 800 pounds } & 5 & \$ 0.34 \
2 & 900 \text { pounds } & 6 & \$ 0.42 \
3 & 700 \text { pounds } & 4 & \$ 0.25
\end{array}$$ 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.
YS1U1B11S1U1B0 = weight loaded in truck 1; YS1U1B12S1U1B0 = weight loaded in truck 2; YS1U1B13S1U1B0 = weight loaded in truck 3;
XS1U1B1i,jS1U1B0 = 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. What formulas should go in cell E26 of the spreadsheet?

Accepted Answer

=SUMPRODUCT(B21:D21,

Question 5

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.

Question 6

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 7

The decision maker has expressed concern with Goal 1, budget, achievement. He indicated that future candidate solutions should stay under budget. How can you modify your goal programming model to accommodate this change?

Accepted Answer

A)  Make budget a hard constraint in the model. 
B)  Give d1+ an extremely large weight in the objective function. 
C)  Remove d1+ from the goal constraint. 
D)  All of these. 
A)  Make budget a hard constraint in the model. 
B)  Give d1+ an extremely large weight in the objective function. 
C)  Remove d1+ from the goal constraint. 
D)  All of these.

Question 8

Consider the following MOLP:
 $\begin{array}{ll}
\text { MAX: } & 3 \mathrm{X}_{1}+4 \mathrm{X}_{2} \
\text { MAX: } & 2 \mathrm{X}_{1}+\mathrm{X}_{2} \
\text { Subject to: } & 6 \mathrm{X}_{1}+13 \mathrm{X}_{2} \leq 78 \
& 12 \mathrm{X}_{1}+9 \mathrm{X}_{2} \leq 108 \
& 8 \mathrm{X}_{1}+10 \mathrm{X}_{2} \leq 80 \
& \mathrm{X}_{1} \mathrm{X}_{2} \geq 0
\end{array}$
 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& @#IMG-DLM& The solution to MAX 3 X₁ + 4

Question 9

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 10

MINIMAX solutions to multi-objective linear programming (MOLP) problems are

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 11

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)  d1- = 0, d1+  = 10 
B)  d1F1F1F1S1?F1F1F10 = 10, d1+  = 0 
C)  d1- = 5, d1+  = 5 
D)  d1- = 6, d1+  = 0 
A)  d1- = 0, d1+  = 10 
B)  d1F1F1F1S1?F1F1F10 = 10, d1+  = 0 
C)  d1- = 5, d1+  = 5 
D)  d1- = 6, d1+  = 0

Question 12

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:
 $\begin{array}{cccc}
\text { Fund } & \text { Rate of return } & \text { Risk } & \text { Minumum investment } \
\hline \mathrm{A} & 12 \% & 0.5 & \$ 20,000 \
\mathrm{~B} & 9 \% & 0.3 & \$ 10.000
\end{array}$
 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:
 $$\begin{array} { l l } 
\text { Let } & \mathbf { X } _ { 1 } = \text { dollars in investment } \mathbf { A } \
& \mathbf { X } _ { \mathbf { 2 } } = \text { dollars } \text { in investment } \mathbf { B } \
\text { MAX: } & \
\text { MiN: } & 0.12 \mathbf { X } _ { 1 } / 50000 + 0.09 \mathbf { X } _ { 2 } / 50000 \
\text { Subject ta: } & 0.5 \mathbf { X } _ { 1 } / 50000 + 0.3 \mathbf { X } _ { \mathbf { 2 } } / 50000 \
& \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } = 50000 \
& \mathbf { X } _ { 1 } \geq 20000 \
& \mathbf { X } _ { \mathbf { 2 } } \geq 10000 \
& \mathbf { X } _ { \mathrm { i } } \geq 0 \text { far all } i
\end{array}$$ 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.
 $\begin{array}{|c|l|c|c|c|}
\hline &{\text { A }} & \mathrm{B} & \mathrm{C} & \mathrm{D} \
\hline 1 & \text { Problem data } & \mathrm{A} & \mathrm{B} & \
\hline 2 & \text { Expected retum } & 12 \% & 9 \% & \
\hline 3 & \text { Risk rating } & 0.50 & 0.20 & \
\hline 4 & & & & \
\hline 5 & \text { Variables } & \mathrm{A} & \mathrm{B} & \text { Total } \
\hline 6 & \text { Amount invested } & \$ 20,000 & \$ 30,000 & \$ 50,000 \
\hline 7 & \text { Minimum required } & \$ 20,000 & \$ 10,000 & \$ 50,000 \
\hline 8 & & & & \
\hline 9 & \text { Objectives: } & & & \
\hline 10 & \text { Average return } & 10.2 \% & & \
\hline 11 & \text { Average risk } & 0.32 & & \
\hline
\end{array}$

Accepted Answer

Question 13

A company needs to supply customers in 3 cities from its 3 warehouses. The supplies, demands and shipping costs are shown below.
 $$\begin{array} { c c c c c } 
&{\quad\quad \text { Destination } } & \
\text { Warehouse } & 1 & 2 & 3 & \text { Supply } \
\hline 1 & 34 & 60 & 36 & 400 \
2 & 70 & 40 & 50 & 300 \
3 & 56 & 40 & 32 & 200 \
\hline \text { Demand } & 500 & 300 & 200 &
\end{array}$$ The company has identified the following goals:
 Goal 1: The company would like to come as close as possible to satisfying its customers demand.
Goal 2:It would also like to ensure that the cost is approximately $ \$ 290.000 $
 Formulate a goal programming model of this problem.

Accepted Answer

The answer of A company needs to supply customers in...

Question 14

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.
  
-Refer to Exhibit 7.1. What formula goes in cell B9?

Accepted Answer

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

Question 15

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)  MIN d3+ 
B)  d3F1F1F1S1F1F1F10 F1F1F1S1F1F1F10 1000 
C)  d3+ = 1000 
D)  d3+ F1F1F1S1F1F1F10 1000 
A)  MIN d3+ 
B)  d3F1F1F1S1F1F1F10 F1F1F1S1F1F1F10 1000 
C)  d3+ = 1000 
D)  d3+ F1F1F1S1F1F1F10 1000

Question 16

A company makes 2 products A and B from 2 resources. The products have the following resource requirements and produce the accompanying profits. The available quantity of resources is also shown in the table.
 $$\begin{array} { l l l c } 
\text { Product } & 1 & 2 & \text { Available resaurces } \
\hline \text { Labor (hr/unit) } & 3 & 2 & 150 \
\text { Material (aunces/unit) } & 1 & 2 & 200 \
\text { Profit( /unit) } & 7 & 6 &
\end{array}$$ Management has developed the following set of goals
 Goal 1: Produce approximately 40 urits of product 1
Goal 2: Produce approxinately 70 urits of product 2
Goal 3: Achieve a profit aver $400.
Goal 4: Consume less than 150 hours of labor
Goal 5:Consume lesse than 200 \text ounces of material 
 Based on the following GP formulation of the problem, and the associated optimal solution, what formulas should go in cells D6:F6, B9:F9, and B16 of the following Excel spreadsheet? NOTE: Formulas are not required in all of these cells.
   $\begin{array}{|c|l|c|c|c|c|c|} 
\hline & {\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \
\hline 1 & \text { Problem Data } & \mathrm{A} & \mathrm{B} & & & \
\hline 2 & \text { Labor } & 3 & 2 & & & \
\hline 3 & \text { Material } & 1 & 2 & & & \
\hline 4 & \text { Profit } & 7 & 6 & & & \
\hline 5 & \text { Goal Constraints } & \mathrm{A} & \mathrm{B} & \text { Labor } & \text { Material } & \text { Profit } \
\hline 6 & \text { Actual Amount } & 4 & 69 & 150 & 142 & 442 \
\hline 7 & + \text { Under } & 36 & 1 & 0 & 58 & 0 \
\hline 8 & - \text { Over } & 0 & 0 & 0 & 0 & 42 \
\hline 9 & =\text { Goal } & 40 & 70 & 150 & 200 & 400 \
\hline 10 & \text { Target Value } & 40 & 70 & 150 & 200 & 400 \
\hline 11 & & & & & & \
\hline 12 & \text { Weights } & & & & & \
\hline 13 & \text { Under } & 1 & 1 & 0 & 0 & 1 \
\hline 14 & \text { Over } & 1 & 1 & 1 & 1 & 0 \
\hline 15 & & & & & & \
\hline 16 & \text { Objective } & 37 & & & & \
\hline
\end{array}$

Accepted Answer

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

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:
 $\begin{array}{cccc}
\text { Fund } & \text { Rate of return } & \text { Risk } & \text { Minimum investment } \
\hline \mathrm{A} & 12 \% & 0.5 & \$ 20,000 \
\mathrm{~B} & 9 \% & 0.3 & \$ 10.000
\end{array}$
 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 18

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.
  
-Refer to Exhibit 7.1. Which cell(s) is(are) the objective cell(s) 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 19

Given the following goal constraints
5 X1 + 6 X2 + 7 X3 + d1F1F1F1S1F1F1F10 F1F1F1S1F1F1F10 d1+ = 87
3 X1 + X2 + 4 X3 + d2F1F1F1S1F1F1F10 F1F1F1S1F1F1F10 d2+ = 37
7 X1 + 3 X2 + 2 X3 + d3F1F1F1S1F1F1F10 F1F1F1S1F1F1F10 d3+ = 72
and solution (X1, X2, X3) = (7, 2, 5), what values do the deviational variables assume?

Accepted Answer

d₁F1F1F1S1^F1F1F10 = 5

Question 20

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.
  
-Refer to Exhibit 7.1. Which cells are the variable cells in this model?

Accepted Answer

A)  $B$6:$C$6, $B$7:$E$8 
B)  $B$6:$C$6 
C)  $B$9:$E$9 
D)  $B$6:$E$8 
A)  $B$6:$C$6, $B$7:$E$8 
B)  $B$6:$C$6 
C)  $B$9:$E$9 
D)  $B$6:$E$8

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

The d_i⁺ variable indicates the amount by which each goal's target value is

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

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

The decision maker has expressed concern with Goal 1, budget, achievement. He indicated that future candidate solutions should stay under budget. How can you modify your goal programming model to accommodate this change?

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

MINIMAX solutions to multi-objective linear programming (MOLP) problems are

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?

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?

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

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

Exam 7: Goal Programming and Multiple Objective Optimization

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

The di+ variable indicates the amount by which each goal's target value is

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

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

The decision maker has expressed concern with Goal 1, budget, achievement. He indicated that future candidate solutions should stay under budget. How can you modify your goal programming model to accommodate this change?

Consider the following MOLP: MAX: 3+4 MAX: 2+ Subject to: 6+13\leq78 12+9\leq108 8+10\leq80 \geq0 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?

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

MINIMAX solutions to multi-objective linear programming (MOLP) problems are

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?

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?

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

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

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

The d_i⁺ variable indicates the amount by which each goal's target value is

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?