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8 year oldMiracle Mattress faced a backlash online after promoting a "twin tower sale", for which every mattress sold on the anniversary of the attacks would be the price of a twin mattress.
At the end of the short clip, staff fall screaming into two large towers of mattress, knocking them over.
"We'll never forget," the presenter of the clip says.
The advert was posted on the company's Facebook page but later deleted.
In a letter, Mike Bonano, the owner of Miracle Mattress, said the video had been produced at the company's San Antonio office without permission from management.
He said: "The video is tasteless and an affront to the men and women who lost their lives on 9/11. Furthermore, it disrespects the families who lost their loved ones and continue to struggle with the pain of this tragedy every day of their lives."
Twitter users criticised the magazine over the video. "This is absolutely sickening," said one. "You deserve to be out of business. End of story," said another.
Many called for the business to remove the video and others for it to shut down.
A total of 2,976 people died on 11 September 2001 when al-Qaeda militants hijacked four planes, crashing two into the World Trade Centre's twin towers, a third into the Pentagon and the fourth into a field in Pennsylvania
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