Reference no: EM13338421

Linear programming models are used bymany Wall Street firms to select a desirable bondportfolio. The following is a simplified version of such amodel. Solodrex is considering investing in four bonds;$1million is available for investment. The expected annualreturn, the worst-case annual return on each bond, and the“duration” of each bond are given in the tablebelow:

               expectedreturn      worst casereturn      duration

bond 1      13%                         6%                        3

bond 2      8%                           8%                        4

bond3      12%                          10%                      7

bond4      14%                           9%                       9

(The duration of a bond is a measure of the bond’s sensitivity to interest rates.) Solodrex wants to maximize theexpected return from its bond investments, subject to threeconstraints: The worst-case return of the bond portfolio mustbe at least 8%. The average duration of the portfolio must be atmost 6. For example, a portfolio that invests $600,000 in bond1 and $400,000 in bond 4 has an average duration of [$600,000(3) +$400,000(9)] / $1,000,000 = 5.4

Because of diversification requirements, at most 40% of the totalamount invested can be invested in a single bond.