Lars Fruergaard Jorgensen has a problem: Too many people want what he’s selling.

Mr. Jorgensen is the chief executive of Novo Nordisk, the Danish drugmaker. Even if the company isn’t quite a household name, the TV jingle for its best-selling drug — “Oh-oh-ohhh, Ozempic!” — might ring in your ears. Across the United States, Novo Nordisk’s diabetes and weight-loss drugs, Ozempic and Wegovy, have soared to celebrity status and helped make the company Europe’s most valuable public firm. It can’t make enough of the drugs.

Mr. Jorgensen’s problem is one many top executives wouldn’t mind, but the success caught him off guard. Last year, when the company was celebrating its centenary, Novo Nordisk’s revenue jumped by a third, to 232 billion Danish kroner, or $33 billion.

“Nobody had forecast this growth — no analyst, nobody in the company,” Mr. Jorgensen said in a recent interview at the company’s headquarters in a suburb of Copenhagen. “Nobody forecast a 100-year-old company would grow more than 30 percent,” he said, seemingly torn between pride and amazement.

For most of its 100 years Novo Nordisk has been focused on the steady business of treating diabetes, one of the world’s most prevalent chronic diseases. Even today, it produces half the world’s insulin. But the development of Ozempic and Wegovy has led to a bigger and bolder ambition to “defeat serious chronic diseases.” That includes treating, and even preventing, obesity, which is linked to other health issues like heart and kidney diseases.

By pursuing a much larger target than diabetes, the company expects to unlock the door to a multibillion-dollar market with nearly a billion potential patients. In the United States alone, more than 40 percent of adults are obese.

And so the Danish drugmaker is undergoing vast changes — it’s getting bigger, more international and closer to the heat of the spotlight. Mr. Jorgensen is trying to ramp up production to meet the huge demand for its weight-loss drugs, stay ahead of competition from Eli Lilly and others and ensure the company’s future so it can meet its lofty goal.

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