George Johnson recently inherited a large sum of money; he wants to use a portio

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 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- Find the optimal solution using the graphical solution procedure.

Please be sure to show all work related to this question. Especially for Part B. I will not rate/give points unless I feel that this has been done.

Explanation / Answer

Let the total amount of the trust fund be T. The amount in the bond fund, B, and the amount in the stock fund, S, will equal the amount of the fund: T = S + B. Also B >= .3T
The return is .06B + .1(T - B) and that is to be >=.075T
.06B + .1T - .1B >= .075T
.025T - .04B >= 0
.025T >= .04B
25T >= 40B
5T >= 8B
B <= .625T
The amount invested in the bond fund should be no more than 62.5% of the total amount, nor less than 30% of the total.

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