Suppose you are restricted to investing in a portfolio of only 2 risky securities. The expected return on security A is 5% and the expected return on security B is 7%. The market portfolio, which is a combination of security A and B, has an expected return of 6%.

a.) Show how to construct an optimal portfolio with an expected return of 9%, assuming there is no risk-free asset.

b.) Show how to construct an optimal portfolio with an expected return of 7%, assuming there is a risk-free asset returning 2%.

c.) Suppose you form a portfolio by making a $10 investment in the risk-free asset and a $60 investment in the market-portfolio. What would the risk-free rate have to be if your portfolio has an expected return of 4%?