PROBLEM: 1 Mathematical models are used by many Wall Street firms in an attempt to select a desirable bond portfolio. The following is a simplified version of such a model. Solodrex is considering investing $1,000,000 in four bonds. The expected annual return, the worst case annual return on each bond, and the "duration" of each bond are given in the Table below. Solodrex wishes to maximize the first year's expected return from its bond investments, subject to the following three constraints: (i) The worst-case return of the bond portfolio in the first year must be at least 8%. (ii) The average duration of the portfolio must be at most 6. For example, a portfolio that invests $400,000 in Bond 1,$400,000 in Bond 2,$200,000 in Bond 3 , and none in Bond 4 would have an average duration of: 1000000400000(3)+400000(4)+200000(7)+0(9)=10000004200000=4.2 (iii) Because of diversification requirements, at most 40% of the total amount invested can be in a single bond. Formulate a Mathematical model that will enable Solodrex to maximize the expected first year return on its investment. Clearly define all decision variables used. (Do not try to solve)