Consider a farmer who plans to sell 6,000 bushels of corns on date T. The date-T spot price of corn is normally distributed with mean $500 per bushel and standard deviation $50 per bushel. To hedge the price risk, the farmer considers shorting corn futures with delivery on date T. The futures price is $480 per bushel, and one contract is to deliver 5,000 bushels. In addition, the farmer can take only integer number of contracts (i.e, a fraction of contract such as 0.1 is NOT allowed).

(a) How may contracts does the farmer need to take?

(b) What is the mean of the total revenue?

(c) What is the standard deviation of the total revenue?