Randy Carr watched the news on his laptop the way you look at a doctor about to administer a shot — nervously and braced for pain. It was April 2, and President Trump was in the Rose Garden about to unveil new tariffs.

An upbeat, slightly jacked 52-year-old, Mr. Carr is the chief executive of World Emblem, a privately held company based in Fort Lauderdale, Fla., that produces about 150 million embroidered patches a year, most of which end up on shirts and hats. He radiates so much energy that even sitting down he appears to be set on vibrate. He’s intense about everything, including his diet, which he described one recent afternoon, karate chopping a tabletop for emphasis.

Two hundred grams of protein a day (bam!), lots of vegetables (bam!), low carbs (bam!), no sugar (bam!). He gets up at 5 a.m. to lift weights every morning and runs five miles every afternoon.

“It’s about being the best I can be every day, for everybody here,” he said. “I wouldn’t want to compete with this company.”

His father started World Emblem in 1990, with two machines in a warehouse in a suburb of Miami. The company’s fortunes were improving by the time it opened a factory in Mexico, in 2005. Today that operation is the size of eight football fields and employs more than 800 people. In a typical week, it produces about 2.5 million emblems.

World Emblem’s factory in Aguascalientes covers eight football fields.Credit…Fred Ramos for The New York Times