2. [Linear Programming – Model Formulation (10 pts)] Eastern Alabama Trust inves
ID: 2747428 • Letter: 2
Question
2. [Linear Programming – Model Formulation (10 pts)] Eastern Alabama Trust invests in various types of securities. A financial advisor there 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.
(a) What are the Decision Variables? (2 pts)
(b) What is the Objective Function? (3 pts)
(c) What are Constraint Equations including non-negativity constraints? (5 pts)
Explanation / Answer
Let A,B,C,D (in thousands)be the amount invested in stock A,B,C,D
max 0.04A+0.06B+0.09C+0.11D
S.t.
A+B+C+D=100
2A+3B+7C+8D<=1000
A<=50, >=20
D>=C
A,B,C,D>=0
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