Julia Johnson has been accumulating savings for years to put toward her children's future college educations. She would now like to set up a college-savings fund for her two children. The college-savings 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 11% for the stock fund. Whatever portion of her accumulated savings that she finally decides to commit to the college-savings fund, she wants to invest at least 30% of that amount in the bond fund. In addition, she wants to select a mix that will enable her to obtain a total return of at least 9%. (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 20 (b) Solve the problem using the graphical solution procedure. What is the value of the objective function at the optimal solution? at (B, S) =

Julia Johnson has been accumulating savings for years to put toward her children's future college educations. She would now like to set up a college-savings fund for her two children. The college-savings 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 11% for the stock fund. Whatever portion of her accumulated savings that she finally decides to commit to the college-savings fund, she wants to invest at least 30% of that amount in the bond fund. In addition, she wants to select a mix that will enable her to obtain a total return of at least 9%. (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 20 (b) Solve the problem using the graphical solution procedure. What is the value of the objective function at the optimal solution? at (B, S) =

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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