Katharine Weymouth, the most powerful person at The Washington Post, was making her way from the elevator bank across the dingy lobby to the exit of the building, a big brutal concrete thing on 15th Street NW. Fred Hiatt, the paper’s editorial page editor, was at the door right before her and almost let it close on her before he realized who she was. There was a big lurch, and with all his arms and legs, he kept the door from slamming on the new publisher.

"Thanks," Ms. Weymouth said. "Getting a coffee and some sunlight!"

"Yeah," Mr. Hiatt said.

Ms. Weymouth has been the New Publisher of The Washington Post for almost six months now. If you didn’t know her, a superficial look on this Friday afternoon would hardly offer the profile of the stereotypical press baron. She’s thin, blond, young for this gig at 42. On this uncharacteristically comfortable summer day in Washington, she was wearing what she called a "Summer Friday" look: a billowy and translucent green-and-white silk blouse from Milly with a wide scoop neck held together in a little tie, with a camisole inset visible underneath. The sleeves ended just about an inch or so off her shoulder, held together by tight elastic, exposing tanned arms. She wore white pants and a plastic white watch covered in rhinestones forming a skull and crossbones pattern. They were a gift from her mother, Lally Weymouth. Her white hite flip-flop heels put her over the 6-foot mark.

The tail end of a long week. And as she walked with a reporter to the nearby Starbucks, she talked about how she planned to spend it: Her three kids, aged 8, 6 and 4, were going to her ex-husband Richard Scully’s house to free her up for a ladies’ night out. This is an annual affair, and a big one, held at a house in Washington.

When she’s blown off all that steam and comes back in on Monday, she once again becomes the scion of one of America’s last great newspaper families. And right now, being a newspaper family is not always a great business proposition.

It was her family—chiefly, Phil Graham, her grandfather, and later his wife, Katharine, who made The Washington Post a quality newspaper. For the past half century, they have molded and shaped it. It was they who brought the paper public; they who established its national and international profile.

What her predecessors did not do—what nobody has been able to do, yet—is figure out how this business will survive in the 21st century.

After 11 years with the Post’s advertising and legal departments, she has spent the past six months in meetings with reporters and editors in the newsroom.

"I have not worked in the newsroom," she said as she settled herself in with her iced coffee. "That’s what I wanted to focus on. I wanted to get an idea of the issues that they’re focused on."

And so she made the controversial decision to move her offices to the fifth floor, where the newsroom is.

"The message I got loudest and clearest was that people fully understand the challenges facing our industry," she said. "But they’re hungry for a sense of, what are we doing about it? Are we just sitting here and praying it’s just going away or are we actually going to take steps to do something about it?"

Well, are we?

"I wish I could say, ‘Here’s the magic bullet! I’ve solved it all! That’s why I took this job, and we’re done, let’s go home,’" she continued. "But that’s not the case."

Ms. Weymouth’s position is not identical to those of her predecessors. About three years after The New York Times brought its Internet and print staffs together to integrate the newsroom, The Post is trying out the same thing. There, the divisions between the two were even deeper than at The Times; this transition has not been, and will continue not to be, an easy one. They still operate from different buildings.

Nor is the overall environment for publishing the news the same.

Editorially the newspaper is riding high. This year, the paper pulled in six Pulitzers, the largest number in the paper’s history. Its newsroom—including online and digital—of nearly 800 is still one of the largest in the country.

But in other ways, that’s just proof that getting the product right is not the last word in this business.

In the past few months, the paper offered buyouts to 100 of its employees in its third round of job cuts in five years. Those who took them included superstars like Tom Ricks, the dominating Pentagon reporter; and Robin Wright, a foreign correspondent. The Post Company’s newspaper division’s operating margin was down 92 percent in the first quarter versus the same time last year, and the company’s operating margin was below 1 percent.

And if Ms. Weymouth projects confidence about the future of the organization, she’s upfront about the lack of specific ideas in the industry, and in her own building, for fixing the business and making the news make money again.

Recently, she took a team of nine Post-ies up to Harvard Business School for an executive leadership course. The Washington Post wasn’t alone—other companies were there, including some from the movie and music industries, and even Halliburton! The course sounded like one big M.B.A. group counseling session: "There is one question they ask—and it’s a great, simple question: If your business went away tomorrow, who would miss you and what would they miss?" she said. "It’s a great question!"

"You have to figure out what the value is to your content and why people come to you," she continued. "I think people come to us because we own Washington. We own politics and Washington. By own—there are lots of other people who do it very well, but I think The Washington Post does have a good value proposition. And that’s judged every day by more than a million people who read us every single day."

She started banging the coffee table.

"That’s a lot of people! So I think we do have a value proposition. But obviously the world is changing. Will there be a print edition in five years? I don’t know the answer to that."

HER THEORY IS exactly right, of course—people still do care about news. But do they care enough about it to buy a newspaper? If she had her way, they’d find a way to make those millions of readers into millions of dollars. Like a good Harvard Business school pupil—"value propositions!"—she says that The Post is a "platform-agnostic" news operation—a term favored by Jonathan Landman, deputy managing editor at The New York Times (and a finalist on Ms. Weymouth’s list of potential executive editors for her own paper when Leonard Downie, executive editor for 17 years, announced he was retiring in the fall). Several times she described The Washington Post as "a newspaper" before correcting herself. "News organization," she’d say.

Asked whether America’s quality newspapers—The Chicago Tribune, the Los Angeles Times, The Wall Street Journal—would always have value, she wanted more clarity.

"I don’t know what you mean by that—do you mean will those particular brands survive? Or the journalism?" she asked.

Well, take the brands, those particular brands.

"Will The Wall Street Journal or The Tribune or the L.A. Times survive? I won’t begin to venture if all the newspaper companies will survive or not. Who knows, right? I hope so. I think the question should not be whether the newspapers survive, but will news organizations survive? And I think the answer is that as long as there are people out there interested in news, there will be entities to provide them the news. I certainly hope and expect that we will make sure that The Washington Post is one of those entities."

But Ms. Weymouth has a curious way of speaking about The Post just as though she had come there out of business school, and not as one of the last scions of a big publishing family at a time when the walls are crashing down on the family media dynasty all over the country.

She retains that slight New York drawl that must have developed in her upbringing on the Upper East Side, on 79th Street off Fifth Avenue. High school was at the Brearley School; she keeps up with the girls she graduated with but doesn’t give money. She went to Harvard as an undergrad, and did stints as a copy girl at The Times, and as an assistant for a Vanity Fair editor for another summer internship, before going to Stanford for law school.

Unlike her grandmother, Katharine Graham, she did not graduate directly from wifely duties to take on the intimidating business of running a newspaper; she was built, educated for and molded into this role in a way nobody ever did for Graham. And consequently the idea of Katharine Weymouth struggling to keep the paper in the family bosom somehow doesn’t fit. For most of the signature moments of the Graham leadership, Ms. Weymouth was a child.

"I don’t remember much about Watergate," she wrote in an email to The Observer. (She was six years old when the scandal broke.) "I remember my mother calling me in to watch Nixon’s resignation, and I remember going to see All The President’s Men."

But she was the only grandchild in the Graham stable to take a job in the company, and she hadn’t been there long before the speculation began.

"A lot of people are saying she’s extremely smart, extremely able, and extremely well respected by the people she works with," Donald Graham told a reporter for The Washingtonian six years ago, when Ms. Weymouth became director of recruitment advertising for the paper. "She does an excellent job."Is she the one? "She’s the only grandchild working in the company at this point. I’ll stick with that."

"I never had a sense that I was being ‘groomed,’ Ms. Weymouth wrote. "It was very important to me that I prove myself at any job I had. I did not worry about where it would lead or have any sense of entitlement. I am very honored that Don has enough confidence in me that he asked me to take on this job and I hope to merit that confidence over time."

In a profile in the forthcoming issue of Portfolio, former Washington Post’s former Reliable Sources columnist Lloyd Grove writes that that was the line Ms. Weymouth’s grandmother took.

"She was optimistic," Stephen Graham, one of Ms. Weymouth’s uncles, told Mr. Grove of his mother’s reaction to Ms. Weymouth’s move in to the family business, "but uttered some cautionary words to the effect that Katharine would have to prove herself on the job, which would be true of any Graham at the Post."

In fact, Ms. Weymouth said, she was very close to her grandmother.

"I socialize with Grandma a lot more than Don [Graham] does," Ms. Weymouth told The New Yorker when she’d been in Washington for a few years. "I like going to parties."

But she has not inherited her grandmother’s taste for social Washington.

"I have three small kids," she said as she sipped her coffee. "I put my kids to bed, I take them to school, I make them dinner whenever I can." Yes, she was going to party hard with her girlfriends later that night, but media parties, she said, like the White House Correspondents Dinner, are "dreadful. I hate them."

She did quote her grandmother once in our interview—"As my grandma used to say: In order to do good, you have to do well," she said of the paper’s finances. But when it comes to business Ms. Weymouth draws more contrast than comparisons to her famous grandparents. And she doesn’t really find herself thinking: What would Kay have done?

"I really knew her much more as a grandma than as a publisher. And our conversations never really revolved around the business decisions she made or challenges she faced."

"She took over at a totally different time," she continued. "She took the company public, the newspaper was growing and I’m not sure she would have had any more answers to what’s happening now than any of the rest of us do."

Ms. Weymouth’s first major act as publisher came on July 7, when she named Marcus Brauchli, the former Wall Street Journal editor, her new chief to replace Len Downie; he became the first editor in decades who didn’t have a relationship with Ben Bradlee. Mr. Brauchli was an editor who tried to play nice with Rupert Murdoch at The Wall Street Journal—he tried to enact a series of changes preemptively in the paper by adding more breaking news to the front page before the takeover was complete—but he was ultimately pushed out anyway after less than a year on the job.

Of the traits Mr. Brauchli brings to the table, which she identified as intelligence and humility, she said the most important was his ability to make hard decisions.

These days in newspaperland, everyone knows what those are.

"Fifteen years ago, 20 years ago when circulation and ad revenues were growing, you didn’t have to make decisions about what do we not cover, or worry about how things have to be allocated," said Ms. Weymouth. "He could probably focus on editing! And shaping stories and deciding who’s going to be on the front page. You didn’t have to think about how does the newspaper interact with online and mobile, and what is the role of the Kindle, and should we do different sorts of content for different platforms."

Since The Post has had only two editors over the past four decades, it’s impossible not to think about the relationship that Katharine Graham had with Ben Bradlee, the two people most responsible for making a mediocre regional newspaper into a national powerhouse. When they had their original interview in 1965, Mr. Bradlee famously told her: "I’d give my left one to be managing editor of The Post."

Ms. Weymouth said there wasn’t any Bradlee-like dramatics in her interviews with Mr. Brauchli.

"There was no one sentence he said, or letter he wrote," she said. "It was really an evolution of everything fitting together of what I was looking for."

"Coming from The Wall Street Journal, he didn’t come in saying, ‘I have a vision for The Washington Post and here’s what I’m going to do!’" she said. "I would have been horrified if he had. He understood that he has worked at a newspaper that has a very different business model and different focus. He appropriately was humble and appreciative of the product we put out and, you know, it’s hard to say. We talked about subjects—everything from an integrated newsroom to the caliber of the content we have."

Ms. Weymouth said she doesn’t like talking to the press, and finds media reporting a little too specifically targeted. In fact, our navel-gazing ways are partly the reason we’re in such a tizzy about the destruction of the newspaper industry.

"Because we are in the newspaper industry, we spend a lot of time writing about the demise of newspapers," she said. "Nobody—I mean, we never see Katie Couric doing a 20-minute segment on the evening news talking about the audience that the nightly news is losing. I mean, they just don’t do those stories, right? We write a little obsessively about our own industry, I think. But when you look at the real story with what’s happening with newspapers, is there a seismic shift going on? Absolutely. Are ad revenues plummeting? Absolutely. But there is still a very good story. We still have a lot of readers, we still have great products and a lot of opportunity."

So it’s overblown?

"This is not me being Pollyannaish," she said. "It’s real. There’s a transition going on. But I think we do have an incredibly powerful story to tell. Look at the numbers of people reading The Washington Post every single day. You walk into a Starbucks every morning and you look at how many people are reading the newspaper, or reading it on their laptops, some on their BlackBerrys. The reason advertisers advertise in the newspaper is not because they’re giving us charity money. It’s because it works! When Marlo’s puts an ad in for a sofa sale, it drives people to their stores, and it drives people to their stores because people are reading the newspaper. Or online."

Wait, isn’t that the old model—the one that seems to be slowly, or not so slowly, crumbling?

"I have been in this job for six months," she said, exasperated. "I’m still learning! We have a team of people that I am leading. But we have a strategy! Our strategy is we are a great political and local newspaper covering the nation’s capital. And we should continue to do that."

So what would Ms. Weymouth miss if The Washington Post went away tomorrow?

An earlier version of this story characterized Len Downie as having taken a buyout from the newspaper to retire this fall; he did not. The Observer regrets the error.