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 11% for the bond fund and 15% 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 12.5%. (a) Formulate a linear programming model that can be used to determine the percentage (as a decimal) that should be allocated to each of the possible investment alternatives. (Assume B is the percentage (as a decimal) of funds invested in the bond fund and S is the percentage (as a decimal) of funds invested in the stock fund.) Max (as a decimal) s.t. bond minimum fund minimum return percentage requirement B, S20 (b) Solve the problem using the graphical solution procedure. What is the value of the objective function at the optimal solution? at (B, S) =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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 11% for the bond fund and 15% 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 12.5%.
(a) Formulate a linear programming model that can be used to determine the percentage (as a decimal) that should be allocated to each of the possible investment alternatives. (Assume B is the percentage (as a
decimal) of funds invested in the bond fund and S is the percentage (as a decimal) of funds invested in the stock fund.)
Max (as a decimal)
s.t.
bond minimum fund
minimum return
percentage requirement
B, S≥ 0
(b) Solve the problem using the graphical solution procedure. What is the value of the objective function at the optimal solution?
at (B, S) =
Transcribed Image Text: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 11% for the bond fund and 15% 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 12.5%. (a) Formulate a linear programming model that can be used to determine the percentage (as a decimal) that should be allocated to each of the possible investment alternatives. (Assume B is the percentage (as a decimal) of funds invested in the bond fund and S is the percentage (as a decimal) of funds invested in the stock fund.) Max (as a decimal) s.t. bond minimum fund minimum return percentage requirement B, S≥ 0 (b) Solve the problem using the graphical solution procedure. What is the value of the objective function at the optimal solution? at (B, S) =
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