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 1000 shares of U.S. Oil. The linear programming formulation that will maximize the total annual return of the portfolio is as follows:Max3U +SHs.t.Maximize total annual return25U + 50H ? 80.000Funds available0.50U + 0.25D ? 700Risk maximum1U? 1000U.S. Oil maximum

FIGURE 3.14 THE SOLUTION FOR THE INVESTMENT ADVISORS PROBLEM Optimal Objective Value = 8400.00000 Variable Value Reduced Cost U 800.00000 0.00000 H 1200.00000 0.00000 Constraint Slack/Surplus Dual Value 1 0.00000 0.09333 2 0.00000 1.33333 3 200.00000 0.00000 Objective Allowable Allowable Variable Coefficient Increase Decrease U 3.00000 7.00000 0.50000 H 5.00000 1.00000 3.50000 RHS Allowable Allowable Constraint Value Increase Decrease l 80000.00000 60000.00000 15000.00000 2 700.00000 75.00000 300.00000 3 1000.00000 Infinite 200.00000 The computer solution of this problem is shown in Figure 3.14. a. \\Vhat is the optimal solution. and what is the value of the total annual retum? b. Which constraints are binding? What is your interpretation of these constraints in terms of the problem? What are the dual values for the constraints? Interpret each. (1. Would it be benecial to increase the maximum amount invested in US. Oil? Why or why not? f"