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Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A particular portfolio consists of U shares of U.S. Oil and H shares of Huber Steel. The annual return for U.S. Oil is $3 per share and the annual return for Huber Steel is $5 per share. U.S. Oil sells for $25 per share and Huber Steel sells for $50 per share. The portfolio has $80,000 to be invested. The portfolio risk index (0.50 per share of U.S. Oil and 0.25 per share for Huber Steel) has a maximum of 700. In addition, the portfolio is limited to a maximum of 1,000 shares of U.S. Oil. The linear programming formulation that will maximize the total annual return of the portfolio is as follows. Maximize total annual return Max 3U+5H s.t. 25U+50H ≤ 80,000 0.50U+0.25H S 700 1U U, Η ΣΟ ≤ 1,000 The computer output is shown below. Optimal Objective Value 8400.00000 Variable U H Constraint 1 2 DE 3 Variable U H Constraint 1 WN. 2 3 Value 800.00000 1200.00000 = Slack/Surplus 0.00000 0.00000 200.00000 3.00000 5.00000 Funds available Risk maximum U.S. Oil maximum Reduced Cost 0.00000 0.00000 RHS Value Objective Allowable Allowable Coefficient. Increase. Decrease 7.00000 0.50000 1.00000 3.50000 80000.00000 700.00000 1000.00000 Dual Value 0.09333 1.33333 0.00000 Allowable Increase 60000.00000 75.00000 Infinite Allowable Decrease 15000.00000 300.00000 200.00000

Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A particular portfolio consists of U shares of U.S. Oil and H shares of Huber Steel. The annual return for U.S. Oil is $3 per share and the annual return for Huber Steel is $5 per share. U.S. Oil sells for $25 per share and Huber Steel sells for $50 per share. The portfolio has $80,000 to be invested. The portfolio risk index (0.50 per share of U.S. Oil and 0.25 per share for Huber Steel) has a maximum of 700. In addition, the portfolio is limited to a maximum of 1,000 shares of U.S. Oil. The linear programming formulation that will maximize the total annual return of the portfolio is as follows. Maximize total annual return Max 3U+5H s.t. 25U+50H ≤ 80,000 0.50U+0.25H S 700 1U U, Η ΣΟ ≤ 1,000 The computer output is shown below. Optimal Objective Value 8400.00000 Variable U H Constraint 1 2 DE 3 Variable U H Constraint 1 WN. 2 3 Value 800.00000 1200.00000 = Slack/Surplus 0.00000 0.00000 200.00000 3.00000 5.00000 Funds available Risk maximum U.S. Oil maximum Reduced Cost 0.00000 0.00000 RHS Value Objective Allowable Allowable Coefficient. Increase. Decrease 7.00000 0.50000 1.00000 3.50000 80000.00000 700.00000 1000.00000 Dual Value 0.09333 1.33333 0.00000 Allowable Increase 60000.00000 75.00000 Infinite Allowable Decrease 15000.00000 300.00000 200.00000

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A particular portfolio consists of U shares of U.S. Oil and H shares of Huber Steel. The annual return for U.S. Oil is $3 per share and the annual return for Huber Steel is $5 per share. U.S. Oil sells for $25 per share and Huber Steel sells for $50 per share. The portfolio has $80,000 to be invested. The portfolio risk index (0.50 per share of U.S. Oil and 0.25 per share for Huber Steel) has a maximum of 700. In addition, the portfolio is limited to a maximum of 1,000 shares of U.S. Oil. The linear programming formulation that will maximize the total annual return of the portfolio is as follows. Maximize total annual return Max 3U + 5H s.t. 25U + 50H ≤ 80,000 0.50U + 0.25H ≤ 700 ≤ 1,000 1U U, H ≥ 0 The computer output is shown below. Optimal Objective Value = 8400.00000 Variable U H Constraint 1 2 3 Variable U H Constraint 1 2 3 Value 800.00000 1200.00000 Slack/Surplus 0.00000 0.00000 200.00000 3.00000 5.00000 Funds available Risk maximum U.S. Oil maximum Reduced Cost 0.00000 0.00000 RHS Value Objective Allowable Allowable Coefficient Increase Decrease 7.00000 0.50000 1.00000 3.50000 80000.00000 700.00000 1000.00000 Dual Value 0.09333 1.33333 0.00000 Allowable Increase 60000.00000 75.00000 Infinite Allowable Decrease 15000.00000 300.00000 200.00000
Transcribed Image Text:Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A particular portfolio consists of U shares of U.S. Oil and H shares of Huber Steel. The annual return for U.S. Oil is $3 per share and the annual return for Huber Steel is $5 per share. U.S. Oil sells for $25 per share and Huber Steel sells for $50 per share. The portfolio has $80,000 to be invested. The portfolio risk index (0.50 per share of U.S. Oil and 0.25 per share for Huber Steel) has a maximum of 700. In addition, the portfolio is limited to a maximum of 1,000 shares of U.S. Oil. The linear programming formulation that will maximize the total annual return of the portfolio is as follows. Maximize total annual return Max 3U + 5H s.t. 25U + 50H ≤ 80,000 0.50U + 0.25H ≤ 700 ≤ 1,000 1U U, H ≥ 0 The computer output is shown below. Optimal Objective Value = 8400.00000 Variable U H Constraint 1 2 3 Variable U H Constraint 1 2 3 Value 800.00000 1200.00000 Slack/Surplus 0.00000 0.00000 200.00000 3.00000 5.00000 Funds available Risk maximum U.S. Oil maximum Reduced Cost 0.00000 0.00000 RHS Value Objective Allowable Allowable Coefficient Increase Decrease 7.00000 0.50000 1.00000 3.50000 80000.00000 700.00000 1000.00000 Dual Value 0.09333 1.33333 0.00000 Allowable Increase 60000.00000 75.00000 Infinite Allowable Decrease 15000.00000 300.00000 200.00000
(a) What is the optimal solution, and what is the value of the total annual return (in $)? U H estimated annual return $ (b) Which constraints are binding? What is your interpretation of these constraints in terms of the problem? (Select all that apply.) Constraint 1. All funds available are being utilized. Constraint 2. The maximum permissible risk is being incurred. Constraint 3. All available shares of U.S. Oil are being purchased. None of the constraints are binding. (c) What are the dual values for the constraints? Interpret each. (Round your answers to two decimal places.) constraint 1 Constraint 1 has a dual value of 3. If an additional dollar is added to the available funds, the total annual return is predicted to increase by $3. O Constraint 1 has a dual value of 1.33. If an additional dollar is added the available funds, the total annual return is predicted to increase by $1.33. O Constraint 1 has a slack of $200. Additional dollars added to the available funds will not improve the total annual return. O Constraint 1 has a dual value of 0.09. If an additional dollar is added to the available funds, the total annual return is predicted to increase by $0.09. O Constraint 1 has a dual value of 5. If an additional dollar is added to the available funds, the total annual return is predicted to increase by $5. constraint 2 Constraint 2 has a dual value of 3. If the risk index is increased by 1, the total annual return is predicted to increase by $3. O Constraint 2 has a dual value of 1.33. If the risk index is increased by 1, the total annual return is predicted to increase by $1.33. O Constraint 2 has a slack of 200. Allowing additional risk will not improve the total annual return. Constraint 2 has a dual value of 0.09. If the risk index is increased by 1, the total annual return is predicted to increase by $0.09. O Constraint 2 has a dual value of 5. If the risk index is increased by 1, the total annual return is predicted to increase by $5. constraint 3 Constraint 3 has a dual value of 3. If the maximum number of shares of U.S. Oil is increased by 1, the total annual return is predicted to increase by $3. O Constraint 3 has a dual value of 1.33. If the maximum number of shares of U.S. Oil is increased by 1, the total annual return is predicted to increase by $1.33. Constraint 3 has a slack of 200 shares. Raising the maximum number of shares of U.S. Oil will not improve the total annual return. O Constraint 3 has a dual value of 0.09. If the maximum number of shares of U.S. Oil is increased by 1, the total annual return is predicted to increase by $0.09. O Constraint 3 has a dual value of 5. If the maximum number of shares of U.S. Oil is increased by 1, the total annual return is predicted to increase by $5.
Transcribed Image Text:(a) What is the optimal solution, and what is the value of the total annual return (in $)? U H estimated annual return $ (b) Which constraints are binding? What is your interpretation of these constraints in terms of the problem? (Select all that apply.) Constraint 1. All funds available are being utilized. Constraint 2. The maximum permissible risk is being incurred. Constraint 3. All available shares of U.S. Oil are being purchased. None of the constraints are binding. (c) What are the dual values for the constraints? Interpret each. (Round your answers to two decimal places.) constraint 1 Constraint 1 has a dual value of 3. If an additional dollar is added to the available funds, the total annual return is predicted to increase by $3. O Constraint 1 has a dual value of 1.33. If an additional dollar is added the available funds, the total annual return is predicted to increase by $1.33. O Constraint 1 has a slack of $200. Additional dollars added to the available funds will not improve the total annual return. O Constraint 1 has a dual value of 0.09. If an additional dollar is added to the available funds, the total annual return is predicted to increase by $0.09. O Constraint 1 has a dual value of 5. If an additional dollar is added to the available funds, the total annual return is predicted to increase by $5. constraint 2 Constraint 2 has a dual value of 3. If the risk index is increased by 1, the total annual return is predicted to increase by $3. O Constraint 2 has a dual value of 1.33. If the risk index is increased by 1, the total annual return is predicted to increase by $1.33. O Constraint 2 has a slack of 200. Allowing additional risk will not improve the total annual return. Constraint 2 has a dual value of 0.09. If the risk index is increased by 1, the total annual return is predicted to increase by $0.09. O Constraint 2 has a dual value of 5. If the risk index is increased by 1, the total annual return is predicted to increase by $5. constraint 3 Constraint 3 has a dual value of 3. If the maximum number of shares of U.S. Oil is increased by 1, the total annual return is predicted to increase by $3. O Constraint 3 has a dual value of 1.33. If the maximum number of shares of U.S. Oil is increased by 1, the total annual return is predicted to increase by $1.33. Constraint 3 has a slack of 200 shares. Raising the maximum number of shares of U.S. Oil will not improve the total annual return. O Constraint 3 has a dual value of 0.09. If the maximum number of shares of U.S. Oil is increased by 1, the total annual return is predicted to increase by $0.09. O Constraint 3 has a dual value of 5. If the maximum number of shares of U.S. Oil is increased by 1, the total annual return is predicted to increase by $5.
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