Ramaco Inc. is a company that specializes in producing aluminum $($or aluminum$).$ The firm produces $10$ million kilograms of aluminum in the first year $($Q$=10$m kg$),$ where the variable cost is $10$ million $($FC $=2/$kg$,$ or U$\_$A$\_$T$4/$kg$,$ with $50\%$ chance for each scenario.In the second year, the firm will consider investing in a project which enables the firm to establish its own plant to use the aluminum foil for automotive applications. The size of the investment $($I$)$ will depend on the total capital it has at the beginning of the second year, which equals to the amount of internal cash flow $($w$)$ it generates during the first year.At the end of the second year, the net value of the project $($i$.$e$.,$ NPV$)$ can be expressed as:F$($I$)=$ f$($I$)$ I $=$I I$2$Assume that m is a random variable that follows a normal distribution, with E$()($i$.$e$.,$ mean of $)=20,$ and $()($i$.$e$.$ standard deviation of $)=2,$ and the correlation coefficient between $$ and market price at the end of the first year, P$,$ is denoted as corr$(,$P$)=.$Assume that at the beginning of the first year, the firm can use a combination of forward and futures contract of the aluminum to hedge against the market risk of the aluminum prices, and the one$-$year forward$/$futures price are U$\_$A$\_$T$3\mathrm{.}0/$kg at the beginning of the first year. Ignore taxes or transaction costs of forwards $/$ futures contract, and assume the discount rate is $0.$Ignore the external capital in this question. Given the range of corr$(,$ P$)$ is between $-1$ to $1,$ what is the resulting range for the optimal hedged quantity of aluminum at the beginning of the first year in the forward or futures contract in terms of maximizing the net value of the firm?Question $13$ options:A$)$between $6\mathrm{.}3524$ millions of kg to $6\mathrm{.}5532$ millions of kg$.$B$)$between $6\mathrm{.}0124$ millions of kg to $6\mathrm{.}2538$ millions of kg$.$C$)$between $6\mathrm{.}2342$ millions of kg to $6\mathrm{.}3553$ millions of kg$.$D$)$between $6\mathrm{.}5526$ millions of kg to $6\mathrm{.}6579$ millions of kg$.$E$)$None of the above