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Let's hope that Jeff Bezos likes cheeseburgers.

Carl's Jr., the fast food franchise known for its smutty ads, is mooching on, Inc. (AMZN) to acquire it through a series of facetious tweets starting early Monday morning, Oct. 9. Along with sister chain Hardee's, the hamburger-and-hot-dog brand could be worth about $1.7 billion, per limited financial information.

The tweets may be silly, but the solicitation for Amazon to buy the chain is entirely serious, a Carl's Jr. spokesman told TheStreet.

Carl's and Hardee's are operated by CKE Restaurant Holdings, Inc. The two chains comprise about 3,000 storefronts in the U.S. After a failed IPO, CKE was purchased by private equity firm Roark Capital Group for between $1.65 billion and $1.75 billion in November 2013.

John Gordon of Pacific Management Consulting estimates CKE could be worth about $1.7 billion, assuming a 10 times multiple on the company's earnings before interest, taxes, depreciation and amortization (EBITDA) that was revealed in a SEC filing in 2012. Gordon thinks the company's valuation has largely stayed unchanged since 2012 due to stagnant same-store sales. 

Carl's Jr.'s average store sales have seen nearly no growth in recent years, according to National Restaurant News' ranking report. In 2016, it posted average store sales of $1.312 million, compared with $1.303 million in 2015.

The restaurant-focused investment firm or Amazon could not be reached for comment.

In the meantime, Carl's Jr. is in full pitch mode.

"Carl's Jr. sees a synergy between Amazon's delivery service and [its own $5] meal boxes that just rolled out," the Carl's Jr. spokesman said. There could also be a partnership opportunity with Amazon's Dash Button for Carl's Jr.'s chicken tenders. In fact, the chain is tweeting out 24 of these "BIG IDEAS" on Monday, according to its twitter.

Some of these so-called "billion-dollar ideas" for Amazon are more outlandish than others. In one tweet, Carl's Jr. drafted a rendering of a"Happy Drone Hive," a dock on top of a Carl's Jr. restaurant for Amazon to deploy its drones.

Amazon could have a more pragmatic use for Carl's, and potentially Hardee's too, according to Gordon: Using the kitchens in the 3,000+ restaurants as food manufacturing and delivery hubs.

As Amazon continues to refine its food delivery programs, he said, "it will need physical spaces to prepare whatever they're doing with their food line."

The Twitter campaign is not the company's first foray into unconventional marketing. In 2005, Carl's launched a series of commercials that featured famous models, clad in bikinis, suggestively eating a burger, with Paris Hilton as the inaugural face of the campaign.

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Editors' pick: Originally published Oct. 9.