Problem $1$

A company wishes to hedge its exposure to a new fuel using gasoline futures contracts. The table below shows data on monthly changes in the new fuel spot price and the gasoline futures price. The company will lose $$2$ million for each $1$ cent decrease in the price per gallon of the new fuel over the next three months. What is the company's position on futures contracts and how many gasoline futures contracts should be traded? Each contract is on $42,000$ gallons.

$\backslash$table$[[\backslash$table$[[$New Fuel$],[$Spot$],[$Price$],[$Change$]],0\mathrm{.}04,0\mathrm{.}15,0\mathrm{.}70,-0\mathrm{.}51,-0\mathrm{.}41,0\mathrm{.}50,0\mathrm{.}61,-0\mathrm{.}22,-0\mathrm{.}35,0\mathrm{.}79],[\backslash$table$[[$Gasoline$],[$Futures$],[$Price$],[$Change$]],-0\mathrm{.}06,0\mathrm{.}01,0\mathrm{.}80,-0\mathrm{.}56,-0\mathrm{.}46,0\mathrm{.}56,0\mathrm{.}63,-0\mathrm{.}12,-0\mathrm{.}44,0\mathrm{.}60]]$