A farmer produces $10,000$ bushels of corn per season, which he sells in September. A good friend of his suggested he sells the whole production in the futures market. The settlement price $($in cents per bushel$)$ for the September corn futures contract is $403\mathrm{.}4($or ${403}^{\text{'}}4$ in CME parlance$)$ and the size of the contract is $5,000$ bushels. The projection indicate the spot price of corn in September will be either $3\mathrm{.}5$ or $4\mathrm{.}5$ Dollars per bushel with equal probability. The farmer is very weary of selling it all in the futures market. What proportion of the production should he sell in the futures market and should he take the long or the short? Calculate the farmer's gains and losses associated with all the combinations of contracts.