Hostess Brands Inc. said yesterday that its snack-cake business would be sold to private equity firms Apollo Global Management LLC and C. Dean Metropoulos & Co after no other bids were received, negating the need for an auction, Reuters reported yesterday. Apollo Global Management and C. Dean Metropoulos in January offered $410 million for the business, which includes Twinkies, Cup Cakes and Suzy Q's. The bid by the private equity firms for the 82-year-old bakery was to serve as the minimum offer for the business, which others could have topped in an auction. Mexico's Grupo Bimbo had been seen as a potential candidate but no other bids materialized.