Suppose that risk-free rate is rf, the expected rate of return on Twitter is u1, the standard deviation of return on Twitter is q1, the expected rate of return on LinkedIn is u2, the standard deviation of return on LinkedIn is q2, and the correlation coefficient between the returns on Twitter and LinkedIn is p. You work for Spartan Wealth Management.

Part 1: You have a client who is interested in investing $100,000 in only Twitter and LinkedIn and he is willing to accept a standard deviation of 15% for his portfolio. Clearly write down the problem whose solution gives you the optimal portfolio for your client. Do not need to solve problem.

Part 2: You have another client who is interested in investing $100,000 in the risky-free asset, Twitter and LinkedIn. Write down the problem whose solution gives you the tangency portfolio for your client. Do not need to solve.