TOPIC: NON-LINEAR PROGRAMMING

Two investors, Elon Musk and Jeff Bezos, each want help in structuring a portfolio from two investments. Investment A produces an average annual return of 25% with a variance of 0.05. Investment B produces an average annual investment of 9% with a variance of 0.01. Investments A and B have a correlation of -0.3. Elon Musk tells you that: "I want to get the biggest return I can, but the most risk I can possibly accept is 0.01. How should I invest my money?" While Jeff Bezos tells you that: "Risk minimisation is half as important as maximising return for me. What portfolio would be most appropriate for me?"

Answer the following questions:

(a) Formulate Elon Musk's problem as a non-linear program.

(b) Calculate the risk aversion coefficient for Jeff Bezos.

(c) Formulate Elon Musk's problem as a non-linear program.