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%.

Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives. If required, round your answers to three decimal places. If the constant is "1" it must be entered in the box.

Let B = percentage of funds invested in the bond fund S=percentage of funds invested in the stock fund

S = percentage of funds invested in the stock fund

B + S

s.t.

B

Bond fund minimum

B + S Minimum return

B+ S Percentage requirement

b. Solve the problem using the graphical solution procedure. If required, round your answers to one decimal place.

Optimal solution: B = , S =

Value of optimal solution is %