7. Investment Advisors, Inc., is a brokerage firm that manages stock portfolios

Question

7. 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:

The sensitivity report for this problem is shown in Figure 8.15.

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 shadow prices for the constraints? Interpret each.

d. Would it be beneficial to increase the maximum amount invested in U.S. Oil? Why or why not?

FIGURE 8.15 SENSITIVITY REPORT FOR THE INVESTMENT ADVISORS PROBLEM

Variable Cells

Model   Final Reduced Objective Allowable Allowable

Variable               Name               final Value             Cost       Coefficient            Increase         Decrease

U                             U.S. Oil 800.000 0.000          3.000                7.000              0.500

H                               Huber 1200.000              0.000          5.000                1.000              3.500

Constraints

Constraint                                      Final                    Shadow      Constraint               Allowable           Allowable

Number               Name               Value                  Price            R.H. Side                   Increase             Decrease

1              Funds available           80000.00       0.093   80000.000            60000.000            15000.000

2              Risk maximum               700.000          1.333               700.000 75.000                       300.000

3              U.S. Oil maximum         800.000         0.000                1000.000              1E?30                       200.000

Explanation / Answer

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