Using futures contract what is the optimal number of, Financial Management

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Using futures contract what is the optimal number of

JetBlue will purchase 5,500,000 gallons of jet fuel in 3 month and wants to hedge with heating oil futures. Heating oil futures contracts are for 42,000 gallons. From historical data σHO = 0.0423, σJF = 0.0383, and ρ = 0.929. Spot price on jet fuel = $1.99 and F0 on heating oil = $2.09.

a. Using futures contract what is the optimal number of contracts to buy or sell?

b. Using forwards contracts what is the optimal number of contracts to buy or sell?

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