Employees of Market Basket are rallying this morning outside the company headquarters in Tewksbury And also today the board of directors for the low-price grocery chain will meet at the Prudential Center. They'll probably discuss a buyout offer from ousted CEO Arthur T Demoulas.

The board's decision may determine the future of Market Basket.

For days the media and general public have been captivated by protesting Market Basket employees who say Arthur T. Demoulas treated them with respect and generosity.

"While everything we've seen going on in the public has been happening, Arthur T. has obviously been out soliciting support," said Scott Latham is the chair of management and strategy at UMass Lowell's Manning School of Businesses.

Latham says it probably wasn't tough for Demoulas to convince investors Market Basket is a smart purchase — the company has no debt and very strong operating cash flows. But he says potential investors would probably be worried the cousin who orchestrated Arthur T. Demoulas' ouster, Arthur S. Demoulas, would continue to make trouble, even in a diminished role.

"This situation at this point for any external investor, is potentially toxic," Latham said. "Because who wants to buy into that feud? So they'd have to have to have assurances that the issues would be settled. And they could get that in black and white, set in stone."

The dollar amount of Arthur T.'s buyout offer for 50.5 percent of the company hasn't been made public — but he says it's fair. Market Basket has probably gotten buyout offers before, when Arthur T. was still on the inside. So that means he knows what other parties are willing to pay for the company.

"So when he says this is a fair offer, he knows it's a fair offer," Latham said. "And so that really turns the screws to the board of directors because it if it really is a fair offer, what do they do?"

And that sets the scene as employees rally outside company headquarters in Tewksbury and, 30 miles away, board members meet at the Prudential Center.

Latham thinks it's unlikely the board will accept Arthur T.'s offer.

"Because I think on some level it would be, 'Boy, he won. Arthur T won, and the employees won.'" he said. "And I don't know that Arthur S. and the board would be willing to do that."

To get past that, Harvard Business School Professor John Davis says someone in the boardroom has to step up and be a diplomat. He says that person must argue that by accepting a buyout, the Arthur S. side of the family will actually be the victor.

"They forced the issue, they were bought out on fair terms, and they won their freedom," he said. "They're no longer captive. And that is the reality. And they should see it that way."

But Davis, who studies the dynamics of family-run businesses, says a peaceful outcome like that is rare.

"Some families, we'll see about this one, but some families are committed to making the other side suffer," he said. "And what often happens when they do that is they destroy the company."

What might be different about the Market Basket situation, Davis says, is the employees.

"I have never seen whole employee groups walk out," he said. "And I have never seen politicians go to bat like they have in this situation. So I think that they're probably a very powerful force, and really make the point that the company has to come first. Family, get your act together, resolve this issue. Be responsible to all these employees and customers, and do the right thing, for God sakes."

Davis says the board of directors has to act quickly, because once customers are lost, it's tough to win them back. The only other option, he says, is for the whole family to sell Market Basket to a third party.

Then the Arthur T and Arthur S wings of the family could go their separate ways.