Washington University uses about 376,394 kWh/year. [1] That's about 7,841.54 kWh/week. Washington pays about 13.1 cents per kWh for power [2]. Running on the electric grid alone this would cost $598.59 per week. This isn't what they pay though, because they offset much of this usage with renewable energy like solar panels.
That would take a 50kw generator to power. Assuming they don't power all systems during a blackout they could probably get away with a 25kw generator. For argument, let's assume a 50kw generator full load would probably use about 4.0 gallons of diesel fuel per hour. [3]
At $3.64/gallon for diesel [4], at 4.0gallons/day, for one week the university's fuel cost would be $2,446.08.
To recap, the university would spend $2,446.08 to generate electricity they could purchase for $598.59 from the electric company during a 7 day blackout at full capacity.
[1] https://www.electricchoice.com/blog/25-of-the-most-energy-ef...
[2] https://www.bls.gov/regions/mid-atlantic/news-release/averag...
[3] https://www.dieselserviceandsupply.com/Diesel_Fuel_Consumpti...