Tyson Foods CEO Donnie Smith is optimistic the company will continue to grow, but he admits that now is not the best time to up production in the United States.

"There is not an availability to buy a lot of eggs or to buy a lot of pullets over the next six months," said Smith. He added that he expected the supply to increase during the last two months of 2013, with the inventory continuing to grow in 2014.

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Smith adds that a lot of hatching eggs from the U.S. are presently being exported to Mexico as the poultry industry there deals with avian influenza problems.

While growth in the U.S. poultry sector will be slow during the upcoming months, Smith said during the BMO Capital Markets 2013 Farm to Market Conference on May 14 that the company is focusing more now on international growth. He said business has been good in Mexico and Brazil, and a lot of potential has been seen in China.