Suppose Intel's stock has an expected return of $20\mathrm{.}0\%$ and a volatility of $3\mathrm{.}0\%,$ while Coca$-$Cola's has an expected return of $7\mathrm{.}0\%$ and volatility of $3\mathrm{.}0\%.$ If these two stocks were perfectly negatively

correlated $($i$.$e$.,$ their correlation coefficient is $-1),$

a$.$ Calculate the portfolio weights that remove all risk.

b$.$ If there are no arbitrage opportunities, what is the risk$-$free rate of interest in this economy?