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 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

1                             80000.00000                      60000.00000           15000.00000

2                              700.00000                           75.00000                   300.00000

3                              1000.00000                         Infinite                       200.00000

programming formulation that will maximize the total annual return of the portfolio is

as follows:

Max 3U + 5H   Maximize total annual returns.t.25U + 50H <= 80000 Funds available 0.50U + 0.25D<= 700 Risk maximum

1U <= 1000 U.S. Oil maximum

The computer solution of this problem is shown in Figure 3.14.

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 values for the constraints? Interpret each.

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

e. calculate the range of optimally for C1, C2