LAKELAND, FLA.—The billionaire daughter of the Publix Super Markets founder has died after having early-onset Alzheimer’s Disease, the company announced Wednesday. Carol Jenkins Barnett was 65. Barnett died Tuesday night at her home in Lakeland, Florida, Publix said in a news release. She was diagnosed with Alzheimer’s in 2016. Barnett was one of seven children of Publix founder George W. Jenkins, who died in 1996. Her net worth was estimated this year at $2.1 billion, according to Forbes magazine. Barnett began working as a cashier at Publix in 1972, eventually serving on its board of directors for 33 years, the company said. She was known in Lakeland—where Publix is based—for her philanthropic work, including financial support for the United Way, the founding of Bonnet Springs Park in Lakeland, a pavilion for women and children at Lakeland Regional Health and many other organizations. “The Publix family is deeply saddened by the …