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. Max 30 + 5H Maximize total annual return S.C. 250 + SOM S 40,000 Funds available 0.500 + 0.25HS 700 Risk maximum 10 $1,000 U.S. Oll maximum U, H2O The computer output is shown below. Optimal best ve Value - 8450.00000 BCU.OC030 1200.000 Redur Car 0.000 0.0000 11 Constraint 7 Slack/Surplus 2.non 9.COOO 209.000on Dual Ve 0.9333 1.13333 1. 1. 11 in 2 3 Watce 6 1414 415 16 . 3. [ LI LIU 5.00300 7.00000 1.00000 THEPH 0.500U 3.50000 F. HLIO.. Allowable 18.in Value Increase Decrease 1 80300.30000 60000.00300 15000.COOCO 700.00000 75.00000 310.CHOCO 1300. 30000 Incerite 200.000 (a) What is the optimal solution, and what is the value of the total annual return (in s)? U estimated annual retum $ (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. 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. Max 30 + 5H Maximize total annual return S.C. 250 + SOM S 40,000 Funds available 0.500 + 0.25HS 700 Risk maximum 10 $1,000 U.S. Oll maximum U, H2O The computer output is shown below. Optimal best ve Value - 8450.00000 BCU.OC030 1200.000 Redur Car 0.000 0.0000 11 Constraint 7 Slack/Surplus 2.non 9.COOO 209.000on Dual Ve 0.9333 1.13333 1. 1. 11 in 2 3 Watce 6 1414 415 16 . 3. [ LI LIU 5.00300 7.00000 1.00000 THEPH 0.500U 3.50000 F. HLIO.. Allowable 18.in Value Increase Decrease 1 80300.30000 60000.00300 15000.COOCO 700.00000 75.00000 310.CHOCO 1300. 30000 Incerite 200.000 (a) What is the optimal solution, and what is the value of the total annual return (in s)? U estimated annual retum $ (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
