Eventually Carol's computer will tell her -"you can't get there from here", but she's not going to tell the PHB that.....BTW, the only thing you get in domestic first class is a larger seat and more peanuts. It's worth the price if you REALLY like peanuts...
Sorry, Helmeet, I think that's exactly what's going on: she's playing him and he doesn't have a clue. Booking an airline ticket may not be fun, but it's not a day's work with the national budget as the price.
Notice that this is probably the first strip with both Carol and PHB that is not about PHB incompetence/obliviousness/phbness and/or Carol payback/deliberate inneficience (in fact she is doing actual work without a hint of cinism)
She is just filling in a web form which the PHB feels his PA should do.
The PHB views her as his PA, but she is only paid receptionist/typist, hence her revenge.
The company once flew me from London to Dallas, being an engineer the ticket was for cattle class, but cost more than business class. Lucky I was bumped up to business (with sleeper seats).