# Thread: Linear Programming Help

1. ## Linear Programming Help

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 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%.
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.
b. Solve the problem using the graphical solution procedure.

2. Originally Posted by psfrag26
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 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%.
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.
b. Solve the problem using the graphical solution procedure.
Introduce two variables $b$ and $s$ to denote the fraction of the available funds invested in each option.

Then the first constraint is:

$b+s \le 1$

Now each clause is a statement about $b$ and $s$ which you need to write as an inequality.

What I don't see here is something clearly identifiable as the objective.

CB

### george johnson recently inherited a large sum of money

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