Basically she's importing time series data from sensors around the production plant, and then doing fairly complex engineering calculations. All of the formulas are pretty much textbook or derivation/substitutions thereof (e.g. different units, etc), but it's really crazy seeing them written as single line Excel expressions. She spends hours debugging single expression errors in the formulas written by herself and other engineers.
Since you asked for 2 examples, I used a spreadsheet for hosting cost estimation.
EDIT: Even if she got it installed she'd have to the whole team to install it as well because they share data by emailing the spreadsheets.
If there is not a hard requirement for the data to be on-site, have you seen Google BigQuery and Fusion Tables?
Notes: These 3 are the main 3 that I have seen. i.e.
1) creating estimates. 2) mini database 3) Science/Stats/engineering calculations
I am working on this: www.cellmaster.com.au - so I ask people what they use spreadsheets for all the time.