Managing a Portfolio. A local bank wants to build a bond portfolio from a set of five bonds with $ 1 million available for investment. The expected annual return, the worst-case annual return on each bond, and the "duration" of each bond are given in the following table. (The duration of a bond is a measure of the bond's sensitivity to changes in interest rates.) Expected Return Worst Case Return Return Duration Bond 1 12. 5% 8. 0% Bond 2 11. 5% 7. 5% Bond 3 10. 5% 6. 8% 6 Bond 4 9. 5% 7. 0% Bond 5 8. 5% 7. 4% The bank wants to maximize the expected return from its bond investments, subject to three conditions: - The average worst-case return for the portfolio must be at least 7. 2 percent. The average duration of the portfolio must be at most 6. Because of diversification requirements, at most 40 percent of the total amount invested can be invested in a single bond. a. What is the maximum return on the $ 1 million investment? How should the investment be distributed among the bonds to achieve this return? (Assume that bonds can be purchased in fractional amounts.) b. What is the qualitative pattern in the optimal solution?