Problem 6(10pt) : 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=0.0263 and F=0.0313, and the correlation between those two prices is =0.928. 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