Problem $6(10$pt$)$: An airline expects to purchase $2$ million gallons of jet fuel in $1$ month and decides to use

heating oil futures, which expire in $1$ month, for hedging. We suppose that the standard deviations for the

jet fuel price and for the heating oil futures are ${}_S=0\mathrm{.}0263$ and ${}_F=0\mathrm{.}0313,$ and the correlation between

those two prices is $=0\mathrm{.}928.$ If each heating oil futures contract is on $42,000$ gallons of heating oil, what is

the optimal number of contracts to achieve minimum variance hedging?