solve foll task in detail with explaination

4- A trader owns 55,000 gallons of jet fuel asset and decides to hedge the value of her position with futures contracts on Nat Gas. Each futures contract is on 5,000 MMBtu. The spot price of the jet fuel is $28/gallon and the standard deviation of the change in this price over the life of the hedge is estimated to be $0.43. The futures price of the Nat Gas is $27 per MMBtu and the standard deviation of the change in this over the life of the hedge is $0.40. The coefficient of correlation between the spot price change and futures price change is 0.95. (a) What is the minimum variance hedge ratio? (b) Should the hedger take a long or short futures position? (c) What is the optimal number of futures contracts when adjustments for daily settlement are not considered?