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 5% for the bond fund and 30% for the stock fund. Whatever portion of the inheritance George finally decides to commit to the trust fund, he wants to invest at least 80% 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 6.5%. 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. Let B = percentage of funds invested in the bond fund S = percentage of funds invested in the stock fund fill in the blank 2 B + fill in the blank 3 S s.t. fill in the blank 4 B fill in the blank 6 Bond fund minimum fill in the blank 7 B + fill in the blank 8 S fill in the blank 10 Minimum return fill in the blank 11 B + fill in the blank 12 S fill in the blank 14 Percentage requirement 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 %

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section11.3: Financial Models

Problem 28P

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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 5% for the bond fund and 30% for the stock fund. Whatever portion of the inheritance George finally decides to commit to the trust fund, he wants to invest at least 80% 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 6.5%.

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.

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

	fill in the blank 2 B	+	fill in the blank 3 S
s.t.
	fill in the blank 4 B			fill in the blank 6	Bond fund minimum
	fill in the blank 7 B	+	fill in the blank 8 S	fill in the blank 10	Minimum return
	fill in the blank 11 B	+	fill in the blank 12 S	fill in the blank 14	Percentage requirement

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 %

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