Question 1

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. Which value should the investor change, and in what direction, if he wants to reduce the risk of the portfolio?
A)D11, increase
B)D12, increase
C)C12, increase
D)D12, decrease

Accepted Answer

The investor should increase the value in cell D12 to reduce the risk of the portfolio. This is because increasing the weight of Investment B (which has a lower risk factor) in the portfolio will decrease the overall risk of the portfolio.

Question 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. Which cell(s) is(are) the target cells in this model?
A)$B$6:$C$6, $B$10:$B$11
B)$B$6:$C$6
C)$B$6:$D$6
D)$B$10:$B$11

Accepted Answer

The answer of  
The following questions are based on...

Question 3

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

The answer of Consider the following MOLP:
  Graph the...

Question 4

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?
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)

Accepted Answer

Cell B11 requires the formula for the total risk factor of the portfolio, which is the weighted average of the risk factors of investments A and B. The formula in cell B11 is =SUMPRODUCT(B3:C3,$B$6:$C$6)/$D$7, where B3:C3 are the risk factors, $B$6:$C$6 are the investment amounts and $D$7 is the total investment amount. This formula calculates the weighted average of the risk factors, which is equal to 0.29. Therefore, the best choice is C.

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. Which cells are the changing cells in this model?
A)$B$6:$C$6, $B$10:$B$11
B)$B$6:$C$6
C)$B$6:$D$6
D)$B$10:$B$11

Accepted Answer

The changing cells in this model are the investment amounts for Investment A and Investment B, which are located in cells $B$6 and $C$6, respectively. The constraints ($B$10:$B$11) set the minimum investment amounts for each investment. Therefore, the best choice is B as it identifies the correct changing cells in the model.

Question 6

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? A)MIN d₃⁺ B)d₃^- $\ge$ 1000 C)d₃⁺ = 1000 D)d₃⁺$\le$ 1000

Accepted Answer

Option D includes a constraint that limits the sum of the cost and the deviation from the budget to be less than or equal to $1000, which meets the manager's objective of not exceeding the budget by more than $1000. Option A, B, and C do not include any such constraint to ensure that the budget is not exceeded by more than $1000.

Question 7

The MINIMAX objective
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.

Accepted Answer

The MINIMAX objective aims to minimize the maximum deviation or worst-case scenario from any goal. This approach is commonly used in decision-making when there is a risk of uncertain outcomes or potential losses. By minimizing the maximum deviation, the decision maker can ensure that the decision will not lead to an outcome that is significantly worse than any other potential outcome.

Question 8

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

Accepted Answer

A solution that cannot be improved in any objective without worsening at least one other objective is known as Pareto optimal. This solution is the best possible solution when optimizing multiple objectives simultaneously.

Question 9

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? 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.

Accepted Answer

Modifying the RHS value in option A does not address the requirement to not exceed the level of 50. Option B changes the constraint to a lesser one which could lead to a less optimal solution. Option D does not take into account the other variables in the model. Therefore, the best option is to add a constraint to limit the value of d₄⁺ to 50 while keeping the original constraint in place. This ensures that the requirement to not exceed the level of 50 is met while still maintaining the original constraints.

Question 10

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

Accepted Answer

The answer of 
The following questions are based on the...

Question 11

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 B10?
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)

Accepted Answer

The correct formula for cell B10, based on the context of calculating a weighted average or similar operation that involves summing products of corresponding entries in two ranges and then dividing by a constant, is =SUMPRODUCT(B2:C2,$B$6:$C$6)/$D$7. This formula multiplies each element in the range B2:C2 with the corresponding element in the range $B$6:$C$6, sums up these products, and then divides the result by the value in cell $D$7.

Question 12

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

Accepted Answer

The formula in cell E11 should calculate the percentage change in value, which is typically done by taking the difference between the new and old values (C11-B11), dividing by the old value (C11), and then multiplying by the quantity (D11) to get the total change.

Question 13

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? 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.

Accepted Answer

The answer of The decision maker has expressed concern with...

Question 14

The primary benefit of a MINIMAX objective function is
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.

Accepted Answer

The primary benefit of a MINIMAX objective function is that it yields a larger variety of solutions than generally available using linear programming (LP) methods. This is because it aims to minimize the maximum regret, allowing for a broader exploration of potential solutions within the feasible region, rather than focusing on optimizing a single linear objective.

Question 15

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

Accepted Answer

The objective cell in this model is $B$20, which represents the total cost of advertising. The goal is to minimize this cost while still reaching the target audience.

Question 16

Given the following goal constraints 5 X₁ + 6 X₂ + 7 X₃ + d₁^-F1F1F1S1-F1F1F10 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

The answer of Given the following goal constraints 5 X₁ +...

Question 17

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

Accepted Answer

The answer of 
The following questions are based on the...

Question 18

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$6?
A)$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

Accepted Answer

The answer of  
The following questions are based on...

Question 19

An optimization technique useful for solving problems with more than one objective function is
A)dual programming.
B)sensitivity analysis.
C)multi-objective linear programming.
D)goal programming.

Accepted Answer

The answer of An optimization technique useful for solving problems...

Question 20

MINIMAX solutions to multi-objective linear programming (MOLP) problems are
A)dually optimal.
B)Pareto optimal.
C)suboptimal.
D)maximally optimal.

Accepted Answer

The minimax solution to a MOLP problem is a solution where the decision maker minimizes the maximum deviation from the desired objective values. This type of solution is also known as a Pareto optimal solution, which means that it is not possible to improve one objective without worsening at least one of the other objectives. Therefore, choice B is correct. Choices A, C, and D do not accurately describe the characteristics of minimax solutions to MOLP problems.

Quiz 7: Goal Programming and Multiple Objective Optimization

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?

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?

The MINIMAX objective

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

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 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 primary benefit of a MINIMAX objective function 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?

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

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