Minimum Price
This contract allows you to sell cash corn for any delivery period, setting a price "floor" but capturing all the upside in the futures through the date the option month expires. 5000 bushel minimum
Example:
In May, you could sell for October delivery at $5.00 but by using the Dec $5.40 Minimum Price you could have the upside of $5.40 Dec futures through November 20th and sell for a Minimum Price of $4.80. For about half of the cost of an "at-the-money" call (in most cases), you can get upside protection beyond your delivery date.
If on August 10th (using the example above), Dec futures are trading at $6.40, you could exercise your premium of +$1.00 on the Minimum Price. This would give you a final sale at $5.80.
Hedge-to-Arrive
This contract allows you to sell the futures for any delivery month and keep the "basis" portion open. You are allowed to roll the HTA once within the crop to a later delivery month for a fee.
Example:
In January, you can sell the Dec (fall delivery) futures for $5.40 or cash corn for $5.00. If you believe basis will "narrow" in that delivery month you could use the HTA to set just the futures level of that sale. Later that summer, carry (spread between futures) has shown you can roll that HTA from December to July at a $0.30 carry and set a basis of -$0.30. In this scenario, $5.40 Dec futures become a July cash sale of $5.40.