Formula for max volume of rectangular bag I'd like a formula for a bag made of two flat equal sized rectangles (e.g. a freezer bag). Assume no stretching, and perfect flexibility. Volume in terms of a and b, the dimensions of the bag when flat. 
Thanks

I think this problem is difficult.  It certainly is difficult if you started with two congruent disks rather than two congruent rectangles.  The disks problem is sometimes known as the Mylar Balloon problem.  See, e.g., "The Mylar Balloon Revisited," 2003, Amer. Math. Monthly (JSTOR link).
See also Igor Pak's 2006 paper, "Inflating polyhedral surfaces" (CiteSeer link).
          
