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. C

Question 2

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:   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, B1:D1) + F17*SUM(B18:D18) + F18*SUM(B22:D22)

Question 3

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. If the company is very concerned about going over the $200,000 budget, which cell value should change and how should it change?

Accepted Answer

A)  D13, increase 
B)  D13, decrease 
C)  D14, increase 
D)  D14, decrease 
A)  D13, increase 
B)  D13, decrease 
C)  D14, increase 
D)  D14, decrease C

Question 4

A dietitian wants to formulate a low cost, high calorie food product for a customer. The following information is available about the 2 ingredients which can be combined to make the food. The customer wants 1000 pounds of the food product and it must contain at least 250 pounds of Food 1 and 300 pounds of Food 2.   Formulate the MOLP for this problem.

Accepted Answer

The answer of A dietitian wants to formulate a low...

Question 5

A company wants to purchase large and small delivery trucks. The company wants to purchase about 10 large and 15 small trucks. Each large truck costs $30,000 and has a 10 ton capacity. Each small truck costs $20,000 and has a 7 ton capacity. The company wants to have about 200 tons of capacity and spend about $600,000.
Based on the following formulation and associated integer solution, what values should go in cells B2:E16 of the spreadsheet?   ​

Accepted Answer

The answer of A company wants to purchase large and...

Question 6

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:   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.   with solution (X1, X2) = (15,370, 34,630).
What values should go in cells B2:D14 of the spreadsheet?

Accepted Answer

Question 7

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 D6?

Accepted Answer

A)  =SUMPRODUCT(B2:B3,B6:B7) 
B)  =B2*C2+B6*C6 
C)  =SUMPRODUCT(B2:C2,B10:C10) 
D)  =SUMPRODUCT(B2:C2,B6:C6) 
A)  =SUMPRODUCT(B2:B3,B6:B7) 
B)  =B2*C2+B6*C6 
C)  =SUMPRODUCT(B2:C2,B10:C10) 
D)  =SUMPRODUCT(B2:C2,B6:C6)

Question 8

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 9

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.  
-Refer to Exhibit 7.2. What formula goes in cell B11?

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$7 
D)  =SUMPRODUCT(B3:C3,$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$7 
D)  =SUMPRODUCT(B3:C3,$B$6:$C$6)

Question 10

Deviational variables

Accepted Answer

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

Question 11

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 ​
40 X1 + 20 X2 + d4− + d4+ = 300
​
To accommodate this requirement?

Accepted Answer

A)  Increase the RHS value from 300 to 350. 
B)  Replace the constraint with 40 X1 + 20 X2 ≤ 350. 
C)  Do not modify the constraint, add a constraint d4+ ≤ 50. 
D)  Do not modify the constraint, add a constraint d4+ = 50. 
A)  Increase the RHS value from 300 to 350. 
B)  Replace the constraint with 40 X1 + 20 X2 ≤ 350. 
C)  Do not modify the constraint, add a constraint d4+ ≤ 50. 
D)  Do not modify the constraint, add a constraint d4+ = 50.

Question 12

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 13

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

Accepted Answer

A)  3X1 + 2 X2 + d1− − d1+ = 10 
B)  3X1 + 2 X2 + d1− + d1+ = 10 
C)  3X1 + 2 X2 − d1− − d1+ ≤ 10 
D)  3X1 + 2 X2 + d1− − d1+ ≥ 10 
A)  3X1 + 2 X2 + d1− − d1+ = 10 
B)  3X1 + 2 X2 + d1− + d1+ = 10 
C)  3X1 + 2 X2 − d1− − d1+ ≤ 10 
D)  3X1 + 2 X2 + d1− − d1+ ≥ 10

Question 14

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 15

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:   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.
Formulate the integer goal programming problem for Robert. (Hint: objective function involves decision and deviation variables.)

Accepted Answer

Y₁ = weight loaded in truck 1;

Question 16

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 17

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)  d1− = 10, d1+ = 0 
C)  d1− = 5, d1+ = 5 
D)  d1− = 6, d1+ = 0 
A)  d1− = 0, d1+ = 10 
B)  d1− = 10, d1+ = 0 
C)  d1− = 5, d1+ = 5 
D)  d1− = 6, d1+ = 0

Question 18

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 19

A constraint which represents a target value for a problem is called a

Accepted Answer

A)  fuzzy constraint. 
B)  vague constraint. 
C)  preference constraint 
D)  soft constraint 
A)  fuzzy constraint. 
B)  vague constraint. 
C)  preference constraint 
D)  soft constraint

Question 20

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.

The primary benefit of a MINIMAX objective function is

Deviational variables

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 40 X₁ + 20 X₂ + d₄− + d₄⁺ = 300 To accommodate this requirement?

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

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

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

A constraint which cannot be violated is called a

What weight would be assigned to a neutral deviational variable?

A constraint which represents a target value for a problem is called a

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

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 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

Deviational variables

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 ​ 40 X1 + 20 X2 + d4− + d4+ = 300 ​ To accommodate this requirement?

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

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

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

A constraint which cannot be violated is called a

What weight would be assigned to a neutral deviational variable?

A constraint which represents a target value for a problem is called a

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

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 Evolutionary Optimization

Regression Analysis

Data Mining

Time Series Forecasting

Introduction to Simulation Using Analytic Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

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 40 X₁ + 20 X₂ + d₄− + d₄⁺ = 300 To accommodate this requirement?

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