Question

Problem 7-25 (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 options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 9% for the bond fund and 20% for the stock fund. Whatever portion of the inheritance George finally decides to commit to the trust fund, he wants to invest at least 60% 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 8.5%.

Answer 1

Answer:

optimal solution is 0.6B + 0.4S

highest possible yield = 13.4%

Explanation:

we have to maximize 0.09B + 0.2S

where:

B = amount invested in bonds

S = amount invested in stocks

constraints:

B ≥ 0.6

B + S = 1

S ≥ 0

0.09B + 0.2S ≥ 0.085

using solver, the optimal solution is 0.6B + 0.4S

the portfolio's yield = (0.6 x 0.09) + (0.4 x 0.2) = 5.4% + 8% = 13.4%