You are an investment adviser. Two of your clients, Gomez and Carol, have asked you to design fully diversified portfolios for them. Gomez wishes to invest in a portfolio with a risk $($standard deviation$)$ of $10\%.$ Carol wishes to invest in a portfolio with a risk $($standard deviation$)$ of $28\%.$ The risk$-$free rate is $4\%.$ The market portfolio has an expected return of $13\%$ and a standard deviation of $16\%.$

a$)$ What portfolio weights should Gomez use? What portfolio weights should Carol use?

b$)$ Calculate their expected returns.

c$)$ Use the CML to calculate their expected returns.