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With the pork industry saddled with a bad case of pig flu, and the beef industry suffering a drought, right now would be a great time to be a chicken farmer.

In the wake of rising beef and pork prices, chicken is now the cheapest protein on the market. Chicken farmers anticipate earning the most in a year since 1996, even accounting for a drop in farm income due to crop surpluses. Demand for poultry has gone up as a result. So much, in fact, that chicken farmers haven't been able to keep up with the increased demand -- and one farmer is struggling to keep up.

"We haven't run out of chickens, but we are sold out, says Ed Fryar, CEO of Ozark Mountain Poultry in Rogers, Arkansas. "The demand has outstripped the available supply for this year."

Fryar goes through approximately 540,000 birds per week, which he says can take anywhere from four to nine weeks to reach market weight. While that sounds fast, increasing production to keep up with increased demand would take significantly longer--about a year and a half.

And that still doesn't change the fact that, for now,  Fryar can't sell what he doesn't have.

"When you're sold out, if you've got a good customer and they order five percent or ten percent more than they normally take, you don't have the birds," he said. "You don't have the meat to send them, and you'd hate to say no to a customer."

Follow Kai Ryssdal at @kairyssdal