“I’ll Eat You Last,” Broadway’s incoming solo show starring Bette Midler, has locked in its theater and dates, skedding an April opening at the Booth Theater.Title will take over the venue from the current revival of “Who’s Afraid of Virginia Woolf?” That production recently pulled back on a previously announced extension of its limited run, with the show now set to shutter March 3. The Midler starrer, a play by John Logan (“Red”) about legendary Hollywood superagent Sue Mengers, also has nailed down its design team, with Scott Pask (sets), Ann Roth (costumes), Hugh Vanstone (lights) and Fitz Patton (sound) all on board. Production marks a return to the Booth for helmer Joe Mantello, whose staging of “Other Desert Cities” played the theater last season. Joining Graydon Carter, Arielle Tepper Madover, James L. Nederlander and the Shubert Org on the producing team are Terry Allen Kramer, Stephanie P. McClelland, Jeffrey Finn, Ruth Hendel, Larry Magid, Jon B. Platt and Scott and Brian Zellinger. April had shaped up into a month packed with star-driven Broadway plays, with a slate that includes Tom Hanks in “Lucky Guy,” Alec Baldwin and Shia LaBeouf in “Orphans” and Nathan Lane in “The Nance.” “I’ll Eat You Last” begins previews April 5 ahead of an April 24 opening.