Alexis Harrington received an inheritance of $95,000, and she is considering two speculative investmentsthe purchase of land and the purchase ofcattle. Each investment would be for 1 year. Under the present (normal) economic conditions, each dollar invested in land will return the principalplus 20% of the principal; each dollar invested in cattle will return the principal plus 30%. However, both investments are relatively risky. If economic conditions were to deteriorate, there is an 18% chance she would lose everything she invested in land and a 30% chance she would loseeverything she invested in cattle. Alexis does not want to lose more than $20,000 (on average). She wants to know how much to invest in eachalternative to maximize the cash value of the investments at the end of 1 year Should all of Alexis's inheritance be invested according to the optimal solution?

Alexis Harrington received an inheritance of $95,000, and she is considering two speculative investmentsthe purchase of land and the purchase ofcattle. Each investment would be for 1 year. Under the present (normal) economic conditions, each dollar invested in land will return the principalplus 20% of the principal; each dollar invested in cattle will return the principal plus 30%. However, both investments are relatively risky. If economic conditions were to deteriorate, there is an 18% chance she would lose everything she invested in land and a 30% chance she would loseeverything she invested in cattle. Alexis does not want to lose more than $20,000 (on average). She wants to know how much to invest in eachalternative to maximize the cash value of the investments at the end of 1 year Should all of Alexis's inheritance be invested according to the optimal solution?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section4.7: Financial Models

Problem 31P

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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
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