Question

Problem 2-25 (Algorithmic) George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment a bond fund and 2) a stock fund. The pro ected returns over the life of the invest ents are 9% or the bond fund and 11%, forthe stock options: 1 nd. hate er portion of the inheritance he finally decides to commit to the trust fund he wants to invest at least 40% of hat amount in the bo d und in addition, he wants at Selecta mix enable him to obtain a total return of at least 9.5%. a. Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives. If required, round your answers to three decimal places. If the constant is "1" it must be entered in the box Let B-percentage of funds invested in the bond fund s-percentage of funds invested in the stock fund 0.11 S 0.09 BI + Max s.t. 1 B Bond fund minimum 2 0.4 1 S 2 0.095Minimum return 1Percentage requirement b. Solve the problem using the graphical solution procedure. If required, round your answers to one decimal place. Optimal solution: B Value of optimal solution is

Answer 1

Let B-percentage of funds invested in the bond fund S-percentage of funds invested in the stock fund 0.09 BI + 0.11 S Max s.t 40-Bond fund minimum 1 B 9.5 0.09 Minimum return B + 00 Percentage requirement must total 100%) 1 S

120 110 10 80 70 (40, 60) 60 50 maximizing points 40 (75, 25) 30 20 10 13 120 130 140 150 160 170 30 -20 -10 010 20 30 40 5060 70 80 90 10 10 20 B-40 30 Optimal solution -40.5- 60 Value of optimal solution is: 0.09*40 + 0.1 1*60 10.2 %