Problem $6$ Rachel wants to invest $$10,000$ in the stock market. She is considering two stocks to buy: $(1)$ Costco with beta of $0\mathrm{.}78$ and expected returns of $9\%,$ and $(2)$ Amazon with beta of $1\mathrm{.}41$ and expected returns of $16\%.$ Her objective is to make sure her portfolio has a beta of $1\mathrm{.}1$ so that she has a slightly higher risk that the average market.

a$)(4$ points$)$ What are the portfolio weights on her portfolio?

b$)(3$ points$)$ What are the dollar values of her investments in Costco and Amazon?

c$)(3$ points$)$ What is her portfolio expected returns?