1-a) An investor has decided to invest a total of $50,000 (maximum) among three investment opportunities: savings certificates, bonds, and stocks. The annual return on each investment is estimated to be 7%, 9% and 14% respectively. The investor does not intend to invest his annual returns. He would like to maximize his returns while investing a minimum of 10,000 in bonds. Also, the investment in stocks should not exceed the combined total investment in bonds and savings certificates. Finally, he should invest between $5000 and $15000 in savings certificates. Formulate a Linear program to assist the investor towards making his investment decisions.
1-b) Now reconsider the same investment of 50,000 with only two options: bonds and stocks. The annual return on each investment is estimated to be 9% for bonds and 14% for stocks. The investor would like to maximize his returns while investing twice the amount he invests for stocks in bonds. Reformulate the LP and use the graphical solution method to obtain the optimal allocation.