A company needs to sell $5$ million pounds of corn syrup in December. The company wants to use corn Futures to hedge its risk, where each contract is for delivery of $5000$ pounds. The spot price of corn is $$24/$pound$,$ the futures price for delivery in December is $$25\mathrm{.}9/$pound$,$ and the futures price for delivery in January is $$26\mathrm{.}3/$pound$.$ Using historical data, the standard deviation of the change in the spot price

of Corn syrup is $0\mathrm{.}436,$ the standard deviation of the change in the corn futures price is $0\mathrm{.}372,$ and the coefficient of correlation between the change in the spot price and the change in the futures price is $0\mathrm{.}97.$

a$.$ What position should the company take?

b$.$ How many contracts should this company get in the chosen positions?

c$.$ Assume that the position is closed out in November. When the position is closed, the spot price of corn syrup is $$23/$pound$,$ the corn futures price for delivery in December is $$24\mathrm{.}5/$pound$,$ and the corn futures price for delivery in January is $$25\mathrm{.}3/$pound$.$ What is the profit or loss for thecompany when closing the position?