A company will lose $80,000 for each 1 cent decrease in the price per gallon of furnace oil (which is used as fuel for ships) over the next two months. The company plans to hedge its exposure to furnace oil with gasoline futures. Furnace oil price changes have a 0.8 correlation with gasoline futures price changes. Furnace oil price changes have a standard deviation of $2.5 and price changes in gasoline futures have a standard deviation of $3.5. Each futures contract is on 60,000 gallons of gasoline.

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

b) What is the company's exposure measured in gallons of furnace oil?

c) How many gasoline futures should be traded?

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

e) Is this a perfect hedge? Why/why not?