Petrochemical Parfum (PP) is concerned about possible increases in the price of heavy fuel oil, which is one of its major inputs. Show how PP can use either options or futures contracts to protect itself against a rise in the price of crude oil. Show how the payoffs in each case would vary if the oil price were $14, $16, or $18 a barrel. What are the advantages and disadvantages for PP of using futures rather than options to reduce risk?