An airline want to buy 1 million gallons of Jet Fuel and decides to hedge the value of its position with future contract on Heating Oil. Each future contract on heating oil is of 5,000 units. The spot price of the Jet Fuel is $2 and the standard deviation of the change in this price over the life of the hedge is estimated to be $0.3. The future price of the related asset is $1.95 and the standard deviation of the change in this over the life of the hedge is $0.35. The coefficient of correlation between the spot price change and the futures price change is 0.95.

- What position should the hedger take?

- What is the optimal number of futures contract with no tailing of the hedge?

- What is the optimal number of future contract with tailing of the hedge?