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.