Fairprice needs to sell 80,000 bushels of apple on May 31st, and wants to use either the May or June futures to hedge its risk. The current spot price is $136 per bushel and May futures are trading for $140 per bushel while the June futures are priced at $142 per bushel. The standard deviation of monthly changes to the spot price of apples is $12.5 per bushel. The standard deviation of monthly changes to the futures price of May apple contracts is $14.3 per bushel, as compared to June futures at $15 and the correlation between spot and futures price changes is 0.74 for both futures. Each contract is for 5,000 bushels of apple. 

Which futures contract should Fairprice use and what strategy should the company follow? (Describe the hedge in detail including opening and closing of the futures.