A financial advisor is about to build an investment portfolio for a client who has $100,000 to invest. The four investments available are A, B, C, and D. Investment A will earn 4 percent and has a risk of two "points" per $1,000 invested
B earns 6 percent with 3 risk points; C earns 9 percent with 7 risk points; and D earns 11 percent with a risk of 8. The client has put the following conditions on the investments: A is to be no more than one-half of the total invested. A cannot be less than 20 percent of the total investment. D cannot be less than C. Total risk points must be at or below 1,000.
Let A be the amount invested in investment A, and define B, C, and D similarly.
Formulate the linear programming model.
Maximize return = 0.04A + 0.06B + 0.09C + 0.11D
Subject to
A + B + C + D = $100,000
.5A -.5B - .5C - .5D ? 0 (rearranged from A ? .5(A + B + C + D))
.8A - .2B -.2C - .2D ? 0 (rearranged from A ? .2 (A + B + C + D))
-C + D ? 0 (rearranged from D ? C)
.002A + .003B + .007C + .008C ? 1000
A, B, C, D ? 0
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