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 8% for the bond fund and 20% for the stock fund. Whatever portion of the inheritance George finally decides to commit to the trust fund, he wants to invest at least 40% 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 5.5%.

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. If required, round your answers to three decimal places. Let B = percentage of funds invested in the bond fund S = percentage of funds invested in the stock fund

1. Max Max Min	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 the answers to one decimal place. Optimal solution:

B =

S =

Value of optimal solution is= %

Answer 1

Let B represent the percentage of funds invested in the bond fund.

Let S represent the percentage of funds invested in the stock fund.

(a) According to the given information, we have the constraints:

Maximum 0.08B + 0.2S

B ≥ 0.4 Bond Fund Minimum

0.08B + 0.2S ≥ 0.055 Minimum Return

B + S = 1 Percentage requirement (All Funds Invested)

B, S ≥ 0

(b)

	B	S		Used	Constraint
	1	0	≥	0.4	0.4
	0.08	0.2	≥	0.152	0.055
	1	1	=	1	1
Decision Variable	0.4	0.6
Maximize	0.08	0.2
Max	0.152

Thus, the Optimal solution is found when B = 0.4, S = 0.6 and Value of optimal solution is = 15.2 %

Value of optimal solution = 0.08B + 0.2S

= 0.08*0.4 + 0.2*0.6 = 0.152 = 15.2%