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Problem 2-25 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. 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 Маx у 0.09 х в+ 0.20 X S s.t. V B 0.6 x Bond fund minimum 0.09 х в+ 0.25 x S > V 0.085 X Minimum return 1 V B 1 V s = v Percentage requirement b. Solve the problem. If required, round your answers to one decimal place. Optimal solution: B = 1 x, S = 1 X Value of optimal solution is X %

Problem 2-25 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. 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 Маx у 0.09 х в+ 0.20 X S s.t. V B 0.6 x Bond fund minimum 0.09 х в+ 0.25 x S > V 0.085 X Minimum return 1 V B 1 V s = v Percentage requirement b. Solve the problem. If required, round your answers to one decimal place. Optimal solution: B = 1 x, S = 1 X Value of optimal solution is X %

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 2-25 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. 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 Маx у 0.09 х в+ 0.20 X S s.t. V B 0.6 x Bond fund minimum 0.09 х в+ 0.25 x S > V 0.085 X Minimum return 1 V B 1 V s = v Percentage requirement b. Solve the problem. If required, round your answers to one decimal place. Optimal solution: B = 1 x, S = 1 X Value of optimal solution is X %
Transcribed Image Text:Problem 2-25 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. 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 Маx у 0.09 х в+ 0.20 X S s.t. V B 0.6 x Bond fund minimum 0.09 х в+ 0.25 x S > V 0.085 X Minimum return 1 V B 1 V s = v Percentage requirement b. Solve the problem. If required, round your answers to one decimal place. Optimal solution: B = 1 x, S = 1 X Value of optimal solution is X %
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