An individual investor has just obtained a $100,000 (after-tax) bonus from her employer and is looking for investment opportunities for these funds. The investor is about five years from retirement and would like to choose investments that are somewhat safe, yet offer a worthwhile return. A close friend of hers who is an investment analyst suggests that the oil industry and steel industry give a great opportunity for return without too much risk in the short-term, and that the remainder of the funds should be invested in government bonds. Her friend has identified the following five alternatives and estimated their annual rates of return:
Investment Projected Rate
Atlantic Oil 9.1%
Pacific Oil 8.3%
Midwest Steel 6.4%
Royal Steel 5.5%
Government Bonds 3.6%
Based upon the advice from her friend, the investor has decided that no more than two-thirds of the total investment should be in oil stocks, and no more than 30% of the total investment should be in steel stocks. In addition, at least $1 must be invested in government bonds for every $5 invested in oil stocks. Also, exactly $3 must be invested in Midwest Steel for every $2 invested in Royal Steel.
With these guidelines, formulate a single LP model to maximize the expected rate of return.