An investor wants to invest up to $100,000 as follows: X amount into a Certificate of Deposit (CD) 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 4, Z amount into a Stock with an expected annual return of 7% and a risk index of 8. The investor’s objective is to maximize the total expected annual return of the investment. However, to be prudent, the investor requires that: The fraction of the total investment in X must be at least 20%. The fraction of the total investment in Z must not exceed 50%. The combined portfolio risk index must not exceed 5. 10.1 (10 points) Set up this investment problem as a linear program, which has 3 variables, 3 basic constraints, and 4 special constraints. 10.2 (5 points) Use an LP software to find the maximum expected annual return in dollars and the dollar values of X, Y, and Z for this best investment. 10.3 (5 points) From the software solution, show the values of the dual variables for the four special constraints.