UPDATE 1-Republic Airways completes Midwest purchase

*Republic paid $6 mln cash, issued $25 mln note

*Midwest to operate as subsidiary

ATLANTA, July 31 - Republic Airways Holdings, which faces competition from Southwest Airlines Co as it seeks to acquire bankrupt Frontier Airlines, said on Friday that it completed the acquisition of Midwest Airlines from Texas private equity group TPG Capital.

Indianapolis-based Republic said it paid TPG $6 million in cash and has issued a $25 million five-year note that can be converted to Republic stock at $10 a share.

The company said Midwest, which is based in Wisconsin, would operate as a Republic unit, flying under its own name.

In a statement, Republic Airways pledged to bring "operational and cost efficiencies" as it looks to grow Midwest.

On Thursday, Southwest Airlines said it submitted a nonbinding proposal to acquire Frontier Airlines for a minimum of $113.6 million, compared with Republic's deal to acquire the carrier for $108.75 million. Southwest said it would study Frontier's books to prepare to put forth a binding bid to be submitted by the bankruptcy court's Aug. 10 deadline.