there's not much reason for there to be a connection between oil and food prices. Some oil is used to transport the food and drive harvesters etc but I suspect those fuel costs are relatively minor. The big hydrocarbon input to food is natural gas which is used to produce fertilizer and various *cides. Costs to farmers for those products are large. This is one of the reasons why companies like MON, DOW, and DD are quite happy with low NG prices.
Most oil is used for transporting humans - not food.
Historically, America’s dairy processors have focused on their home markets, but many of them have retooled in the past decade, boosting output to help supply infant formula, cheese and other products to China and other countries with rapidly expanding middle classes.
…Exports now account for the equivalent of about 16% of U.S. milk production, up from 5.7% in 2003.