Instead of the labs, gyms and other rooms standing empty during the shutdown, the same isolation of people could be achieved by allocating each building or other resource to one person. Equipment from gyms or labs could be lent out for the duration of the shutdown, of course keeping a database of who borrowed what and making the borrower liable for its safe return. If only one person uses each object or building the whole time, then there is no cross-contamination or infection-spreading.
Excess demand could be rationed by lottery. Only the winner of the lottery for a resource would be allowed to use the resource, with large penalties for sharing. This would improve efficiency slightly, because one person instead of zero would be using each resource.
If the heat, water and electricity were turned off during the shutdown, then it might be more efficient to let the buildings stand empty, instead of having the utilities on and one person in each building or room. However, the lights in MIT buildings are still on at night, just like before the shutdown (and it seemed wasteful back then already).