A financial advisor is about to build an investment portfolio for a client who h

Question

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. Upload your LP formulation in a pdf file format.

Explanation / Answer

Solution

Maximize Z = 0.04A + 0.06B + 0.09C + 0.11D

Subject to

A + B + C + D 100000

A (A + B + C + D)/2 or A - B - C – D 0

A 0.2(A + B + C + D) or 8A - 2B - 2C – 2D 0

D – C 0

(2A/1000) + (3B/1000) + (7C/1000) + (8D/1000) 1000 or

2A + 3B + 7C + 8D 1000000

A, B, C, D 0. DONE

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