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Unformatted text preview: Example Problem, 2.25 Investment Analysis: George Johnson recently inherited a large sum of money; he wishes to use some of this money to set up a trust fund for his children. The trust fund has two investments: a bond fund and a stock fund. The estimated returns over the life of the investment are 6% for the bond fund and 10 % for the stock fund. Whatever portion of the inheritance he decides to commit to the trust fund, he wishes to invest at least 30% in the bond fund. In addition he wishes to have an investment mix that will provide a overall 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. (b) Solve the LP and determine the optimal value of the objective Investment Analysis Investment Analysis
Max R(B,S) = 0.06 B+ 0.10 S s.t. C.1 B ≥ 0.3 Bond fund minimum
C.2 0.06 B+ 0.10 S ≥ 0.075 Minimum total return
C.3 B + S = 1 Percentage requirement SOLUTION TO INVESTMENT PROBLEM
MAX 0.06B+0.1S S.T.
Objective Function Value = 0.088
Variable Value Reduced Costs B 0.300
S 0.700 0.000
Constraint Slack/Surplus Dual Prices 1 0.000 ‐0.040
2 0.013 0.000
3 0.000 0.100
OBJECTIVE COEFFICIENT RANGES
Variable Lower Limit Current Value Upper Limit
B No Lower Limit 0.060 0.100
S 0.060 0.100 No Upper Limit
RIGHT HAND SIDE RANGES
Constraint Lower Limit Current Value Upper Limit
1 0.000 0.300 0.625
2 No Lower Limit 0.075 0.088
3 0.870 1.000 No Upper Limit ...
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- Spring '10