George Johnson recently inherited a large sum of money; he wants to use a portio
ID: 1169953 • Letter: G
Question
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 9% for the bond fund and 11% for the stock fund. Whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest at least 40% 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 9.5%.
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.
Solve the problem. If required, round the answers to one decimal place.
Optimal solution: B = , S =
Value of optimal solution is %
Explanation / Answer
Answer)
LPP structure ,
Max Z= 0.09B + 0.11 S
Subject to
B>= 0.40
Clearly Indicate with one constraint ,
The maximum return =10.2 % at B= 40% and S= 60%.
Let B 0.4 percentage of funds invested in the bond fund S 0.6 percentage of funds invested in the stock fund B + S Return s.t. Bond fund minimum 40% 40% + 60% 10.2 Minimum return 10.2 41% 59% 10.18 42% 58% 10.16 43% 57% 10.14 44% 56% 10.12 45% 55% 10.1 46% 54% 10.08 47% 53% 10.06 48% + 52% 10.04 49% 51% 10.02 50% 50% 10 51% 49% 9.98 52% 48% 9.96 53% 47% 9.94 54% 46% 9.92 55% 45% 9.9 56% + 44% 9.88 57% 43% 9.86 58% 42% 9.84 59% 41% 9.82 60% 40% 9.8 61% + 39% 9.78 62% 38% 9.76 63% 37% 9.74 64% 36% 9.72 65% 35% 9.7 66% 34% 9.68 67% + 33% 9.66 68% 32% 9.64 69% 31% 9.62 70% 30% 9.6 71% 29% 9.58 72% 28% 9.56 73% + 27% 9.54 74% 26% 9.52 75% 25% 9.5 B + S Percentage requirement 9.5Related Questions
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