Question 1

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. Which cells are the changing 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

Question 2

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.

Question 3

A constraint which cannot be violated is called a

Accepted Answer

A)  binding constraint. 
B)  hard constraint. 
C)  definite constraint. 
D)  required constraint.

Question 4

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 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)

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:
 $$\begin{array} { c c c c } 
\text { Truck } & \text { Weight Capacity } & \text { Box Capacity } & \text { Cast per pound } \
\hline 1 & \text { 800 pounds } & 5 & \$ 0.34 \
2 & 900 \text { pounds } & 6 & \$ 0.42 \
3 & 700 \text { pounds } & 4 & \$ 0.25
\end{array}$$ 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. Based on the integer goal programming formulation, the associated solution, and spreadsheet model, what formulas should go in cells B19:E19 and B24:E24 of the spreadsheet?

Accepted Answer

The answer of Exhibit 7.4
The following questions are based on...

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:
 $\begin{array}{cccc}
\text { Fund } & \text { Rate of return } & \text { Risk } & \text { Minimum investment } \
\hline \mathrm{A} & 12 \% & 0.5 & \$ 20,000 \
\mathrm{~B} & 9 \% & 0.3 & \$ 10,000
\end{array}$
 Note that a low Risk rating means a less risky investment. The investor 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.
Formulate a goal programming model with a MINIMAX objective function.

Accepted Answer

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

Question 7

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. 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 answer of Exhibit 7.4
The following questions are based on...

Question 8

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 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$6F1F1F1S1?F1F1F10$B$7:$C$7 
C)  $B$6:$C$6F1F1F1S1?F1F1F10$B$7:$C$7 
D)  $B$6:$C$6=$D$7

Question 9

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

Accepted Answer

The answer of Robert Gardner runs a small, local-only delivery...

Question 10

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 of the following is a constraint specified to Risk Solver Platform (RSP) for this model?

Accepted Answer

A)  $B$9:$E$9=$B$6:$E$6 
B)  $B$9:$E$9$B$10:$E$10

Question 11

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 goal programming formulation, associated solution, and spreadsheet model, what formulas should go in cells D6:E6, B9:E9, and B16 of the spreadsheet?
  $\begin{array}{|c|l|c|c|c|c|}
\hline &{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } \
\hline 1 & \text { Problem Data } & \text { Large } & \text { Small } & & \
\hline 2 & \text { Cost } & 10 & 7 & & \
\hline 3 & \text { Capacity } & 30 & 20 & & \
\hline 4 & & & & & \
\hline 5 & \text { Goal Constraints } & \text { Large } & \text { Small } & \text { Cost } & \text { Capacity } \
\hline 6 & \text { Actual Amount } & 10 & 15 & 205 & 600 \
\hline 7 & \text { + Under } & 0 & 0 & 0 & 0 \
\hline 8 & \text { - Over } & 0 & 0 & 5 & 0 \
\hline 9 & =\text { Goal } & 10 & 15 & 200 & 600 \
\hline 10 & \text { Target Value } & 10 & 15 & 200 & 600 \
\hline 11 & & & & & \
\hline 12 & \text { Weights } & & & & \
\hline 13 & \text { Under } & 1 & 1 & 1 & 1 \
\hline 14 & \text { Over } & 1 & 1 & 1 & 1 \
\hline 15 & & & & & \
\hline 16 & \text { Objective } & 5 & & & \
\hline
\end{array}$

Accepted Answer

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

Question 12

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.
 $\begin{array}{lllc}
\text { Product } & 1 & 2 & \text { Avalable resources } \
\hline \text { Labor (hr/unit) } & 3 & 2 & 150 \
\text { Material (ounces/unit) } & 1 & 2 & 200 \
\text { Profit(\$/unit) } & 7 & 6 &
\end{array}$
 Management has developed the following set of goals
 Goal 1: Produce approximately 40 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 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 13

Which of the following are true regarding weights assigned to deviational variables?

Accepted Answer

A)  The weights assigned can be negative. 
B)  The weights assigned must sum to one. 
C)  The weight assigned to the deviation under a particular goal must be the same as the weight assigned to the deviation above that particular goal. 
D)  All of these are false.

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.

Question 15

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.
 $\begin{array}{lccc}
\text { Product } & \text { A } & \text { B } & \text { Avalable resources } \
\hline \text { Labor (hr/unit) } & 3 & 2 & 150 \
\text { Material (ounces/unit) } & 1 & 2 & 200 \
\text { Profit(\$/unit) } & 7 & 6 &
\end{array}$
 Management has developed the following set of goals
 Goal 1: Produce approximately 40 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 Formulate a goal programming model of this problem.

Accepted Answer

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

Question 16

What weight would be assigned to a neutral deviational variable?

Accepted Answer

A)  0 
B)  1 
C)  10 
D)  100

Question 17

A dietician 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 should contain 250 pounds of Food 1 and 300 pounds of Food 2. The final cost of the blend should be about $1.15 and contain about 2500 calories per pound. The percent of fat, protein, carbohydrate in each food is summarized below with the target values for the goals. The dietician would prefer the food product be low in fat while also high in protein and carbohydrates.
 $\begin{array}{lccc}
& \text { Food 1}&\text { Food 2}& \text { TARGET}\ 
\hline \text { Cost }(\$ / \text { pound) } & \$ 1.00 & \$ 1.25 & \$ 1.15 \
\text { Fat } & 15 \% & 25 \% & 300 \text { pounds } \
\text { Protein } & 35 \% & 40 \% & 370 \text { pounds } \
\text { Carbohydrate } & 50 \% & 35 \% & 400 \text { pounds } \
\text { Calories/pound } & 3000 & 2000 & 2500 \
\text { Pounds of food 1 } & & & 250 \
\text { Pnunds of food2 } & & & 300\end{array}$

Formulate the GP for this problem

Accepted Answer

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

Question 18

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

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.

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

Question 20

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: $\begin{array}{cccc} \text { Fund } & \text { Rate of return } & \text { Risk } & \text { Minimum investment } \ \hline \mathrm{A} & 12 \% & .5 & \$ 20,000 \ \mathrm{~B} & 9 \% & 3 & \$ 10.000 \end{array}$ 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: $\begin{array} { l l } \text { Let } & \mathbf { X } _ { 1 } = \text { dollars in investment } \mathbf { A } \ & \mathbf { X } _ { \mathbf { 2 } } = \text { dollars } \text { in investment } \mathbf { B } \ \end{array}$ $\begin{array}{ll} \text { MAX: } & 0.12 \mathrm{X}_{1} / 50000+0.09 \mathrm{X}_{2} / 50000 \ \text { MIN: } & 0.5 \mathrm{X}_{1} / 50000+0.3 \mathrm{X}_{2} / 50000 \ \text { Subject to: } & \mathrm{X}_{1}+\mathrm{X}_{2}=500000 \ & \mathrm{X}_{1} \geq 20000 \ & \mathrm{X}_{2} \geq 10000 \ & \mathrm{X}_{\mathrm{i}} \geq 0 \text { for all } \mathrm{i} \end{array}$ 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? $\begin{array}{|c|l|c|c|c|} \hline & {\text { A }} & \text { B } & \text { C } & \text { D } \ \hline 1 & \text { Problem data } & \text { A } & \text { B } & \ \hline 2 & \text { Expected retum } & & & \ \hline 3 & \text { Risk rating } & & & \ \hline 4 & & & & \ \hline 5 & \text { Variables } & \text { A } & \text { B } & \text { Total } \ \hline 6 & \text { Amount invested } & & & \ \hline 7 & \text { Minimum required } & & & \ \hline 8 & & & & \ \hline 9 & \text { Objectives: } & & & \ \hline 10 & \text { Average return } & & & \ \hline 11 & \text { Average risk } & & & \ \hline \end{array}$

Accepted Answer

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

Exam 7: Goal Programming and Multiple Objective Optimization

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

Which of the following are true regarding weights assigned to deviational variables?

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

What weight would be assigned to a neutral deviational variable?

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

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

Exam 7: Goal Programming and Multiple Objective Optimization

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

Which of the following are true regarding weights assigned to deviational variables?

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

What weight would be assigned to a neutral deviational variable?

What is the meaning of the ti term in this objective function for a goal programming problem? MIN⁡∑1ti(di−+di+) 2\operatorname { MIN } \sum \frac { 1 } { t _ { i } } \left( d _ { i } ^ { - } + d _ { i } ^ { + } \right) ^ { 2 }MIN∑ti​1​(di−​+di+​) 2

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

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