Many calculus books ask something like, "Ignoring its width and height, find the longest rod that can be moved around a 90 degree corner where 2 halls meet, if the hall is 5 feet wide on one side and 7 feet wide on the other." (See "before the activity")
Before the Activity
This problem helps if you're moving very, very long pieces of uncooked spaghetti and it gives good insight into moving long pieces of ½ inch diameter pipe. But what if you have to move a desk or a sofa? You certainly can't ignore their widths. There is a more general solution that has more meaning to more real problems if you do not ignore the width. See Fig. 1 in the attached PDF file.
See the attached Activity PDF file(s) for detailed instructions for this activity.
During the Activity
Follow the procedures outlined in the activity.
Use the graphing calculator to find the solution to a complex optimization problem.
After the Activity
Review student results
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary