NOTE: I posed this problem at the end of last semester and no one attempted it. It was the first week of finals -- what was I thinking! I'm repeating it now because it's such a wonderful problem that I would like to get you all to think about it again.

Also since our Fall Break takes up the first half of this week, the problem will remain up for two weeks. Enjoy!

Ignoring the weight, a package will be accepted for shipping by the United Parcel Service if its length plus girth is no larger than 130 inches.  See figure on the left.  (The length is the longest dimension while the girth is twice the sum of the other two dimensions.)

What is the size of the square window of smallest area through which you can pass all acceptable packages?

For a heartier meal:  What is the size of the rectangular window of smallest area though which you can pass all acceptable packages?