An airline expects to purchase 4.8 million gallons of jet fuel in one month's time. Because there is no futures contract on jet fuel it decides to use the futures contraction heating oil that trades on the New York Merchantile Exchange. The correlation between monthly changes in the price of jet fuel and monthly changes in heating oil futures is 0.9. The variance of monthly changes in the heating oil futures price per gallon is 0.024 and the variance of the monthly changes in the price of jet oil per gallon is 0.021. A heating oil futures contract is on 50,000 gallons of heating oil.
(a) What is the optimal hedge ratio?
(b) How many contracts should the company buy?