3. (10 points) Today American Airlines wishes to hedge its exposure to changes in the jet fuel price by using heating oil futures. It expects to purchase 798,000 gallons of jet fuel in 3 months (on May 15, 2021) in the spot market and decides to use June 2021 heating oil futures for hedging. Historical market price data shows that (over a period of 3 months) changes in the jet fuel spot price have a 0.881 correlation with heating oil futures price changes, and the changes in the heating oil futures price have a standard deviation that is 20% lower than the standard deviation of spot price changes in jet fuel. The contract size of heating oil futures is 42,000 gallons, and June 2021 heating oil futures currently trade at $1.72 per gallon. (a) If June 2021 heating oil futures are used to hedge the exposure, what should the minimum variance hedge ratio be? (b) In how many June 2021 futures contracts should the company go long? Suppose that on May 15, 2021, the jet fuel spot price is $1.60 per gallon, and the company closes out its position in the futures contracts at a then prevailing June 2021 heating oil futures price of $1.73 per gallon. (c) What would be the company's total P&L from its trade in the futures contract on May 15, 2021, in this scenario