A person wants to invest all of $10,000 into stocks: a high-tech company (T) with an expected annual return of 12% and a risk index of 8; and a regulated power company (P) with an expected annual return of 6% and a risk index of 2. To limit risk, the combined portfolio risk must be no more than 6 and the proportion of investment in T must be less than 70%.

To find the best investment portfolio that maximizes the total annual return R, the LP formulation with return in the unit of full percentage and investment in the unit of thousand dollars is as follows:

Maximize R = 12T+6P

                             T+   P=10 (Constraint 1 on total investment)

                            8T+2P<=60 (Result of Constraint 2 on portfolio risk index)

                              T       <=7 (Result of Constraint 3 on percentage investment in the high-tech company)

                              T, P   >=0

The solution for the LP software shows the following:

T=6.667, P=3.333, R=100.

Furthermore, the dual variable values for the constraints are:

Constraint         Dual Variable

1                                4

2                                 1

3                                 0

E1. (5 points) What is the maximum annual return R in dollars?

E2. (5 points) What is the meaning of the dual variable or shadow price of Constraint 1 on the total investment? You need to be precise in your explanation to get the points. (One way to understand the meaning is to run the LP program with a $1K increase in the total investment and see the impact on the total return.)

E3. (5 points) What is the meaning of the shadow price of Constraint 2 on the portfolio risk index?

E4. (5 points) What is the meaning of the shadow price of Constraint 3 on the percentage investment in the high-tech company? Why is it 0?

Answer rating: 100% (QA)

E1 Max annual return 12 T 6 P 0126667 0063333 1 thousand 1000 E2 Th... View the full answer