A financial planner wants to design a portfolio of investments for a client. The client has $300,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 25% of the money in any one investment, at least one third should be invested in long-term bonds which mature in seven or more years, and no more than 25% of the total money should be invested in C or D since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio. Years To investment Return Maturity Rating
A 6.45% 9 1-Excellent
B 7.10% 8 2-Very Good
C 8.20% 5 4-Fair
D 9.00% 8 3-Good
Let
X1 = Dollars invested in A
X2 = Dollars invested in B
X3 = Dollars invested in C
X4 = Dollars invested in D
MAX: .0645 X1 + .071 X2 + .082 X3 + .09 X4
Subject to: X1 + X2 + X3 + X4 ≤ 300000 X1 ≤ 75000
X2 ≤ 75000
X3 ≤ 75000
X4 ≤ 75000
X1 + X2 + X4 ≥ 100000
X3 + X4 ≤ 75000
X1, X2, X3, X4 ≥ 0