I can't help you a whole lot. Is there anything written on the back? The photo appears to be from the early 1940's. I found a listing of Nebraska Photographers (http://www.rootsweb.com/~neasc/photog/a-g.txt) however "DeLuxe" is not listed there. It's possible the photographer was one of the "De___" people. The two older women are clearly related (most likely mother and daughter) and the younger (she has a "saucy" look doesn't she? I'd love to have known her!) one is likely the daughter of the middle aged woman 9they share a nose). Look in other photos for things like the general placement of the mouth and shape of eyes (I would say ears too, but in this case there is only one showing - very inconvenient!) - and more so the placement of the part in the hair. Women tended to do their hair the same their entire lives up until the 1930's-40's when everyone decided that fashion was in, but the part will be the same. See if anyone else is wearing that pendant the middle-aged woman has on. note the slope and height of the foreheads. Compare it to other pictures you have of identified people.
Good luck, I feel your pain, I have some from the mid-late 1800's which may never be id'd.

Maer