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 8% for the bond fund and 11% 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 amou
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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 8% for the bond fund and 11% 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 9%.
(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)
0.08B+0.11S
s.t.bond minimum fund
minimum return
percentage requirement
B, S ≥ 0
(b)
Solve the problem using the graphical solution procedure. What is the value of the objective function at the optimal solution?
at (B, S) =
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