2. Hedging Using Futures

Consider a farmer who plans to sell 6,000 bushels of corns on dateT. The date-Tspot 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 dateT. The futures price is$480 per bushel, and one contract is to deliver 5,000 bushels. In addition, the farmer can takeonly integernumber of contracts (i.e, a fraction of contract such as 0.1 is NOT allowed).

(a) How many 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?

Answer three parts with detailed steps please.