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?

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

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?

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)

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?

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 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

Exam 7: Goal Programming and Multiple Objective Optimization

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. A 1 Problem data 2 Expected retun 12\% 10\% 3 Risk rating 0.50 0.20 4 5 Variables Tatal 6 Amount invested 0 0 0 7 Minimum required \ 10,000 \ 15,000 \ 150,000 8 9 Objectives: 10 Average return 0 11 Average risk 0 -Refer to Exhibit 7.2. Which cells are the changing cells in this model?

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Question 21

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

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Question 22

A constraint which cannot be violated is called a

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Question 23

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. A 1 Problem data 2 Expected retun 12\% 10\% 3 Risk rating 0.50 0.20 4 5 Variables Tatal 6 Amount invested 0 0 0 7 Minimum required \ 10,000 \ 15,000 \ 150,000 8 9 Objectives: 10 Average return 0 11 Average risk 0 -Refer to Exhibit 7.2. What formula goes in cell B11?

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Question 24

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: Truck Weight Capacity Box Capacity Cast per pound 1 800 pounds 5 \ 0.34 2 900 pounds 6 \ 0.42 3 700 pounds 4 \ 0.25 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. Y₁ = weight loaded in truck 1; Y₂ = weight loaded in truck 2; Y₃ = weight loaded in truck 3; X_i,j = 0 if truck i not loaded with box j; 1 if truck i loaded with box j. $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 $0.10 per pound cost for trucks carrying less weight. The following integer goal programming formulation applies to his problem. Y1 = weight loaded in truck 1; Y2 = weight loaded in truck 2; Y3 = weight loaded in truck 3; Xi,j = 0 if truck i not loaded with box j; 1 if truck i loaded with box j. Given the following spreadsheet solution of this integer goal programming formulation, answer the following questions. -Refer to Exhibit 7.4. Based on the integer goal programming formulation, the associated solution, and spreadsheet model, what formulas should go in cells B19:E19 and B24:E24 of the spreadsheet?$ Given the following spreadsheet solution of this integer goal programming formulation, answer the following questions. $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 $0.10 per pound cost for trucks carrying less weight. The following integer goal programming formulation applies to his problem. Y1 = weight loaded in truck 1; Y2 = weight loaded in truck 2; Y3 = weight loaded in truck 3; Xi,j = 0 if truck i not loaded with box j; 1 if truck i loaded with box j. Given the following spreadsheet solution of this integer goal programming formulation, answer the following questions. -Refer to Exhibit 7.4. Based on the integer goal programming formulation, the associated solution, and spreadsheet model, what formulas should go in cells B19:E19 and B24:E24 of the spreadsheet?$ -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?

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Question 25

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: Fund Rate of return Risk Minimum investment 12\% 0.5 \ 20,000 9\% 0.3 \ 10,000 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.

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Question 26

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: Truck Weight Capacity Box Capacity Cast per pound 1 800 pounds 5 \ 0.34 2 900 pounds 6 \ 0.42 3 700 pounds 4 \ 0.25 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. Y₁ = weight loaded in truck 1; Y₂ = weight loaded in truck 2; Y₃ = weight loaded in truck 3; X_i,j = 0 if truck i not loaded with box j; 1 if truck i loaded with box j. $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 $0.10 per pound cost for trucks carrying less weight. The following integer goal programming formulation applies to his problem. Y1 = weight loaded in truck 1; Y2 = weight loaded in truck 2; Y3 = weight loaded in truck 3; Xi,j = 0 if truck i not loaded with box j; 1 if truck i loaded with box j. Given the following spreadsheet solution of this integer goal programming formulation, answer the following questions. -Refer to Exhibit 7.4. The spreadsheet model has scaled all the weights from pounds into 100s pounds. How does this scaling effect the solution obtained using the Risk Solver Platform (RSP)?$ Given the following spreadsheet solution of this integer goal programming formulation, answer the following questions. $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 $0.10 per pound cost for trucks carrying less weight. The following integer goal programming formulation applies to his problem. Y1 = weight loaded in truck 1; Y2 = weight loaded in truck 2; Y3 = weight loaded in truck 3; Xi,j = 0 if truck i not loaded with box j; 1 if truck i loaded with box j. Given the following spreadsheet solution of this integer goal programming formulation, answer the following questions. -Refer to Exhibit 7.4. The spreadsheet model has scaled all the weights from pounds into 100s pounds. How does this scaling effect the solution obtained using the Risk Solver Platform (RSP)?$ -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)?

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Question 27

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. A 1 Problem data 2 Expected retun 12\% 10\% 3 Risk rating 0.50 0.20 4 5 Variables Tatal 6 Amount invested 0 0 0 7 Minimum required \ 10,000 \ 15,000 \ 150,000 8 9 Objectives: 10 Average return 0 11 Average risk 0 -Refer to Exhibit 7.2. What Risk Solver Platform (RSP) constraint involves cells $B$6:$C$6?

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Question 28

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: Truck Weight Capacity Box Capacity Cast per pound 1 800 pounds 5 \ 0.34 2 900 pounds 6 \ 0.42 3 700 pounds 4 \ 0.25 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.)

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Question 29

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?

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Question 30

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? $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 $600,000. Based on the following goal programming formulation, associated solution, and spreadsheet model, what formulas should go in cells D6:E6, B9:E9, and B16 of the spreadsheet? \begin{array}{|c|l|c|c|c|c|} \hline &{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } \\ \hline 1 & \text { Problem Data } & \text { Large } & \text { Small } & & \\ \hline 2 & \text { Cost } & 10 & 7 & & \\ \hline 3 & \text { Capacity } & 30 & 20 & & \\ \hline 4 & & & & & \\ \hline 5 & \text { Goal Constraints } & \text { Large } & \text { Small } & \text { Cost } & \text { Capacity } \\ \hline 6 & \text { Actual Amount } & 10 & 15 & 205 & 600 \\ \hline 7 & \text { + Under } & 0 & 0 & 0 & 0 \\ \hline 8 & \text { - Over } & 0 & 0 & 5 & 0 \\ \hline 9 & =\text { Goal } & 10 & 15 & 200 & 600 \\ \hline 10 & \text { Target Value } & 10 & 15 & 200 & 600 \\ \hline 11 & & & & & \\ \hline 12 & \text { Weights } & & & & \\ \hline 13 & \text { Under } & 1 & 1 & 1 & 1 \\ \hline 14 & \text { Over } & 1 & 1 & 1 & 1 \\ \hline 15 & & & & & \\ \hline 16 & \text { Objective } & 5 & & & \\ \hline \end{array}$ A B C D E 1 Problem Data Large Small 2 Cost 10 7 3 Capacity 30 20 4 5 Goal Constraints Large Small Cost Capacity 6 Actual Amount 10 15 205 600 7 + Under 0 0 0 0 8 - Over 0 0 5 0 9 = Goal 10 15 200 600 10 Target Value 10 15 200 600 11 12 Weights 13 Under 1 1 1 1 14 Over 1 1 1 1 15 16 Objective 5

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Question 31

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. Product 1 2 Avalable resources Labor (hr/unit) 3 2 150 Material (ounces/unit) 1 2 200 Profit( \/ unit) 7 6 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? $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 $400. Goal 4: Consume less than 150 hours of labor Goal 5:Consume lesse than 200 \text ounces of material Based on this GP formulation of the problem and the associated optimal integer solution what values should go in cells B2:F16 of the following Excel spreadsheet?$ $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 $400. Goal 4: Consume less than 150 hours of labor Goal 5:Consume lesse than 200 \text ounces of material Based on this GP formulation of the problem and the associated optimal integer solution what values should go in cells B2:F16 of the following Excel spreadsheet?$

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Question 32

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

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Question 33

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

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Question 34

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. Product A B Avalable resources Labor (hr/unit) 3 2 150 Material (ounces/unit) 1 2 200 Profit( \/ unit) 7 6 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.

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Question 35

What weight would be assigned to a neutral deviational variable?

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Question 36

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. Food 1 Food 2 TARGET Cost (\ / pound) \ 1.00 \ 1.25 \ 1.15 Fat 15\% 25\% 300 pounds Protein 35\% 40\% 370 pounds Carbohydrate 50\% 35\% 400 pounds Calories/pound 3000 2000 2500 Pounds of food 1 250 Pnunds of food2 300 Formulate the GP for this problem

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Question 37

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

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Question 38

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

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Question 39

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: Fund Rate of return Risk Minimum investment 12\% .5 \ 20,000 9\% 3 \ 10.000 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: Let = dollars in investment = dollars in investment MAX: 0.12/50000+0.09/50000 MIN: 0.5/50000+0.3/50000 Subject to: +=500000 \geq20000 \geq10000 \geq0 for all 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? A B C D 1 Problem data A B 2 Expected retum 3 Risk rating 4 5 Variables A B Total 6 Amount invested 7 Minimum required 8 9 Objectives: 10 Average return 11 Average risk

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Question 40

Showing 21 - 40 of 59

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

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

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

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