Question 1

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 2

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 3

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 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:
   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 5

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 Risk Solver Platform (RSP) constraint involves cells $B$6:$C$6?

Accepted Answer

A) $B$6:$C$6=$B$7:$C$7 
B) $B$6:$C$6$\ge$$B$7:$C$7 
C) $B$6:$C$6$\le$$B$7:$C$7 
D) $B$6:$C$6=$D$7 
A) $B$6:$C$6=$B$7:$C$7 
B) $B$6:$C$6$\ge$$B$7:$C$7 
C) $B$6:$C$6$\le$$B$7:$C$7 
D) $B$6:$C$6=$D$7

Question 6

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 7

The MINIMAX objective

Accepted Answer

A) yields the smallest possible deviations. 
B) minimizes the maximum deviation from any goal. 
C) chooses the deviation which has the largest value. 
D) maximizes the minimum value of goal attainment. 
A) yields the smallest possible deviations. 
B) minimizes the maximum deviation from any goal. 
C) chooses the deviation which has the largest value. 
D) maximizes the minimum value of goal attainment.

Question 8

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. Which cell(s) is(are) 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 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

Exhibit 7.3
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 minimax formulation of the problem has been solved in Excel.
  
-Refer to Exhibit 7.3. What formula goes in cell E11?

Accepted Answer

A) =D11*(C11-B11)/C11 
B) =(C11-B11)/C11 
C) =D11*C11 
D) =D11*(C11- B11) 
A) =D11*(C11-B11)/C11 
B) =(C11-B11)/C11 
C) =D11*C11 
D) =D11*(C11- B11)

Question 11

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 12

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 13

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.   Management has developed the following set of goals
   Based on this GP formulation of the problem and the associated optimal integer solution what values should go in cells B2:F16 of the following Excel spreadsheet?

Accepted Answer

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

Question 14

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 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

Suppose that X1 equals 4. What are the values for d1+ and d1- in the following constraint? X1 + d11-F1F1F1S1-F1F1F10 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

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:
   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

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.   Management has developed the following set of goals
   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.

Accepted Answer

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

Question 19

Consider the following MOLP:
   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 20

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 $\le$ 350. 
C) Do not modify the constraint, add a constraint d4+ $\le$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 $\le$ 350. 
C) Do not modify the constraint, add a constraint d4+ $\le$50. 
D) Do not modify the constraint, add a constraint d4+ = 50.

A constraint which cannot be violated is called a

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

Which of the following is true regarding goal programming?

The MINIMAX objective

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

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?

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

Suppose that X₁ equals 4. What are the values for d₁⁺ and d₁^-in the following constraint? X₁ + d₁1^-- d₁⁺ = 8

Consider the following MOLP: 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?

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?

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

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Exam 7: Goal Programming and Multiple Objective Optimization

A constraint which cannot be violated is called a

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

Which of the following is true regarding goal programming?

The MINIMAX objective

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

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?

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

Suppose that X1 equals 4. What are the values for d1+ and d1- in the following constraint? X1 + d11-- d1+ = 8

Consider the following MOLP: 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?

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?

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 + d₁1^-- d₁⁺ = 8

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?