A company will lose $50,000 for each 1 cent increase in the price per gallon of jet fuel over the next two months. The company plans to hedge its exposure to jet fuel with oil futures. Jet fuel price changes have a 0.85 correlation with oil futures price changes. Jet fuel price changes have a standard deviation of $2.5 and price changes in oil futures have a standard deviation of $3.0. Each futures contract is on 50,000 gallons of oil.

a) What is the optimal hedge ratio? What does this hedge ratio mean?

b) What is the company's exposure measured in gallons of jet fuel?

c) How many oil futures should be traded?

d) Should the company take long or short futures positions? Why?