George Johnson recently inherited a large sum of money; he wantsto use a portion of this money to set up a trust fund for his twochildren. The trust fund has two investment options: (1) a bondfund and (2) a stock fund. The projected returns over the life ofthe investments are 8% for the bond fund and 20% for the stockfund. Whatever portion of the inheritance George finally decides tocommit to the trust fund, he wants to invest at least 40% of thatamount in the bond fund. In addition, he wants to select a mix thatwill enable him to obtain a total return of at least 5.5%.
a.Formulate a linear programming model that can be used todetermine the percentage that should be allocated to each of thepossible investment alternatives. If required, round your answersto three decimal places. Let B = percentage of funds invested inthe bond fund S = percentage of funds invested in the stockfund
| Max | 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. Ifrequired, round the answers to one decimal place. Optimalsolution:
B =
S =
Value of optimal solution is= %
