An investor wants to invest up to $100,000 as follows:

• X amount into a Certificate of Deposit that yields an expected annual return of 1% with a risk index of 1,

• Y amount into a Bond with an expected annual return of 3% and a risk index of 5,

• Z amount into a Stock with an expected annual return of 5% and a risk index of 8.

The investors objective is to maximize the total expected annual return of the investment.

However, to be prudent, the investor requires that:

1. The fraction of the total investment in X must be at least 30%.

2. The fraction of the total investment in Y must be at least 40% but not exceed 60%

3. The fraction of the total investment in Z must not exceed 50%

The combined portfolio risk index must not exceed 6.

QUESTION:

a. Formulate this investment problem as a linear program.

b. In the solution, the combine portfolio risk index is 4.7, what is the value of the dual variable for this constraint?