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Broadway musical “The Last Ship” will close later this month despite a last-ditch effort to drum up sales with an acting stint for Sting, the show’s composer.

“Last Ship” will shutter Jan. 24, when Sting finishes up his limited run in the show. Since the musician began appearing in the production last month, “Last Ship” has logged its best weekly numbers so far — but not numbers spectacular enough to convince producers to hold on through the sales dip certain to come when Sting exits the show during what is traditionally a slow winter period on Broadway.

“Last Ship,” a semi-autobiographical tale about the residents of a dying shipbuilding town in England, received mixed but largely respectful notices, especially for Sting’s music. But it’s had trouble attracting attention from theatergoers in a crowded slate of musicals both new (“Aladdin,” “Beautiful”) and old (“The Lion King,” “Wicked”).

Sting, who had diligently promoted “Last Ship” in the run-up to opening, took on a role in the show to attract bigger crowds over the tourism-fueled holiday season, in the hopes that the influx of audiences would kickstart a sales momentum that would endure after he left.

But now, without the promise of blockbuster sales, producers have decided to throw in the towel, closing the show Jan. 24 and hoping to recoup some of their losses in the licensing market. Jeffrey Seller (“Avenue Q,” “Rent,” “In the Heights”) leads a producing team that also includes Kathryn Schenker, Kevin McCollum, Sander Jacobs, James L. Nederlander, Roy Furman, Herb Alpert and Jerry Moss.