25. 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 op- tions: (1) a bond fund and (2) a stock fund. The projected returns over the life of the in- vestments are 6% for the bond fund and 10% 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 7.5%.
Assuming t is the amount invested in the trust and b is the portion invested in bonds, then 0.06b + 0.1(t - b) represents the projected total return and would make a plausible objective function. It makes sense to want to maximize projected return subject to some bound on risk. However, the same expression will also appear in one of the constraints. Does this help?