Mutual Co is considering investing in four bonds. $1M is available for investment, all of which is to be used. The expected return, the worst-case annual return for each bond, and the "duration" of each bond is shown. The worst-case return of the bond portfolio must be at least 8%. The average duration of the portfolio must be at most 6 . For example, a portfolio that invested $600K in bond 1 and $400K in bond 4 would have an average duration of [$600K(3)+400K(9)/$1M]=5.4. At most 40% of the total amount invested can be invested in bond 1 . The total amount invested in bond 2 cannot be more than 1/3 of the total amount invested in bonds 3 and 4 combined. The amount invested in bond 3 cannot be $50,000 more or less than the amount invested in bond 1 . The \% of money invested in bond 4 must be equal to the % of money invested in bond 1 and 2 combined. Formulate an LP to help Mutual to maximize the expected return on investments. (10 marks)