The United States Postal Service is planning to buy $12,600,000$ gallons of refined

gasoline in December $2023.$ The current spot price of refined gasoline is $$2\mathrm{.}50$ per gallon and

the current December $2023$ futures price is $$2\mathrm{.}24.$ Each futures contract is written on $42,000$

gallons. What futures position should USPS take to hedge its exposure $($i$.$e$.,$ long or short

position and number of contracts$)?$ What is their outcome in the physical market, futures

market, and total outcome if the spot price in December $2023$ ends up being $$2\mathrm{.}12?$ How

about if the spot price in December $2023$ ends up at $$2\mathrm{.}58?$