A portfolio manager is trying to balance investments between bonds, stocks and cash. The return on stocks is 12 percent, 9 percent on bonds, and 3 percent on cash
The total portfolio is $1 billion, and he or she must keep 10 percent in cash in accordance with company policy. The fund's prospectus promises that stocks cannot exceed 75 percent of the portfolio, and the ratio of stocks to bonds must equal two. Formulate this investment decision as a linear programming problem, defining fully your decision variables and then giving the objective function and constraints.
Let X1 = the amount invested in bonds
X2 = the amount invested in stocks
X3 = the amount invested in cash
Max: z = .09X1 + .12X2 + .03X3
s.t. X1 + X2 + X3 ≤ 1,000,000,000 Portfolio value
X1 = 100,000,000 10% minimum stock
X2 ≤ 750,000,000 75% maximum cash
2X1 - X2 = 0 2:1 ratio stocks to bonds
X1, X2, X3 > 0
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