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 + 5H Maximize total annual return

s.t.

25U + 50H ≤ 80,000 Funds available

0.50U + 0.25H ≤ 700 Risk maximum

1U ≤ 1000 U.S. Oil maximum

U, H ≥ 0

The computer solution of this problem is shown in Figure.

THE MANAGEMENT SCIENTIST SOLUTION FOR THE INVESTMENT

ADVISORS PROBLEM

a. What is the optimal solution, and what is the value of the total annual return?
b. Which constraints are binding? What is your interpretation of these constraints in terms of the problem?
c. What are the dual prices for the constraints? Interpret each.
d. Would it be beneficial to increase the maximum amount invested in U.S. Oil? Why or whynot?

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Objective Function Value 8400.000 Variable Value Reduced Costs 800.000 1200.000 0.000 0.000 Constraint Slack/Surplus Dual Prices 0.000 0.000 200.000 0.093 1.333 0.000 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit 2.500 1.500 3.000 5.000 10.000 6.000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit 65000.000 400.000 800.000 80000.000 700.000 1000.000 140000.000 775.000 No Upper Limit