Question 31 25 pts A1. 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 5, Z amount into a Stock with an expected annual return of 5% 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 30%. The fraction of the total investment in Y must be at least 40% but not exceed 60%. The fraction of the total investment in Z must not exceed 50%. The combined portfolio risk index must not exceed 6. A1a. (15 points) Formulate this investment problem as a linear program by using decimal point numbers for percentages of return and dollars for the investment amount (5 points deducted for any incorrect or missing eleme of the formulation). Alb. (5 points) For the total investment constraint, the value of the dual variable in the solution is $0.03. What is additional annual return if the total investment is increased by $1,000? Alc. (5 points) In the solution, the combined portfolio risk index is 4.7. What is the value of the dual variable for constraint? Question 31 25 pts A1. 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 5, Z amount into a Stock with an expected annual return of 5% 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 30%. The fraction of the total investment in Y must be at least 40% but not exceed 60%. The fraction of the total investment in Z must not exceed 50%. The combined portfolio risk index must not exceed 6. A1a. (15 points) Formulate this investment problem as a linear program by using decimal point numbers for percentages of return and dollars for the investment amount (5 points deducted for any incorrect or missing eleme of the formulation). Alb. (5 points) For the total investment constraint, the value of the dual variable in the solution is $0.03. What is additional annual return if the total investment is increased by $1,000? Alc. (5 points) In the solution, the combined portfolio risk index is 4.7. What is the value of the dual variable for constraint
