"My biggest challenge is just to get the cars. We could have sold a lot more if we had the supply," Porsche Cars North America chief Detlev von Platen told Reuters at the Detroit Auto Show on Monday.

He said on average he had 30 days of supply of inventory with the Cayenne SUV coming with less than ten days of supply for that model.

"We would like to have 45 days for the 911 sports car and 60 for the Cayenne ideally," he said.

Von Platen said Porsche was investing $100 million in the United States over the next couple of years, for example, to build test tracks for customers, one in Los Angeles and one in Atlanta, by the end of 2013.

(Reporting By Christiaan Hetzner)