Question

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 options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 13% for the bond fund and 15% for the stock fund. Whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest at least 30% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 14%. (a) Formulate a linear programming model that can be used to determine the percentage (as a decimal) that should be allocated to each of the possible investment alternatives. (Assume B is the percentage (as a decimal) of funds invested in the bond fund and S is the percentage (as a decimal) of funds invested in the stock fund.) Max (as a decimal) s.t. bond minimum fund minimum return percentage requirement B, S 20 (b) Solve the problem using the graphical solution procedure. What is the value of the objective function at the optimal solution? at (B, S) =

Answer 1

B = 30 BI+S=1 1 Q (0.3, 0.7) P(0.5, 0.5) -0.5 0.13 B + 0.15 S 0 0.5 1.5

(a) let 'B' is & 6s is Then proportion invested in bonds pro portion invested in stocks. 0.13B_+ 0.15 S Max lz) = Sit. o.za BH (Bond minimum fund) 0.13 B + 0.15 S 70. 14 (minimum return) Bts I lercentage requirement) B, Szo (b) Corner-points P 10.5, 0.5) Q10.3, 0.7 ZE 0.13 B +0.155 2014 0.144 Optimal in ventment in Bonds = 30% in Stocks = 70% & optimal return 14.4% CS Scanned with CamScanner