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How do you formulate this as a goal programming problem

by | Dec 1, 2023 | Posted Questions

How do you formulate this as a goal programming problem

Mick Garcia, a certified financial planner (CFP) has been
asked by a client to invest $250,000. This money may be placed in stocks,
bonds, or a mutual fund in real estate. The expected return on investment is
13% for stocks, 8% for bonds, and 10% for real estate. 
While the client would
like a very high expected return, she would be satisfied with a 10% expected
return on her money. Due to risk considerations, several goals have been established
to keep the risk at an acceptable level. One goal is to put at least 30% of the
money in bonds. 
Another goal is that the amount of money in real estate should
not exceed 50% of the money invested in stocks and bonds combined. In addition
to these goals, there is one absolute restriction. Under no circumstances
should more than $150,000 be invested in any one area.

How do you formulate this as a goal programming problem?
Assume that all of the goals are equally important.

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