B$.$ The table below shows various information for securities $C$ and $Z$ and for the market

index. The alphas reflect security analysis that the manager of a fund has done on these

two securities$.$ The manager wants to hold the market portfolio, but also wants to put

some money in $C$ and $Z$ to reflect her security analysis. Assume that the excess return on

the market portfolio is $6\%.$

I. Calculate the covariance and betas of $C$ and $Z$ with respect to the market

portfolio.

II$.$ Calculate the systematic and idiosyncratic variance of $C$ and $Z.$

III. Calculate the optimal weight that the manager would assign to the active

portfolio, which is comprised by securities $C$ and $Z,$ and to the market portfolio.

Please answer questions and provide detailed explanations on part III, as it is the one im struggling with. Thank you