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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 %

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter10: Systems Of Equations And Inequalities
Section10.FOM: Focus On Modeling: Linear Programming
Problem 14P
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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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