Sterne Agee analyst Vijay Rakesh is expecting Apple to really ramp up its iPad production. In a note to clients he says his checks with the company’s supply chain finds that the company has been been producing the tablet at a rate of 1-1.5 million units a month, higher than most estimates.

“Barron’s” ( reports that the analyst predicts production could crank up to 2.5 million units a month or more in the September quarter. He says that some previous manufacturing bottlenecks have been solved, though memory remains “a constraint.”

Rakesh also says that checks indicate that new iPhones are coming in the September quarter. In fact, some pundits are expecting ’em to debut at next month’s Apple Worldwide Developer Conference.