Uder what condition is it both possible and profitable ro practise price discrimination

Who is a discriminating monipolist

Yuo've hit on at least a partial answer to your own question. A monopolist can charge different custoners different prices for the same good or servixe, and so his profits can be maximized by pricing such that gross margin per unit times volume is maxized. For example: utilities typically charge different rates for residential versus commercial customers. Airlines try to discrimiate in their pricing by charging more for passengers who make last minute changes and/or who fly round-trip within a week, assuming these customers to be business travelers as opposed to tourists (who can relatively easily change their plans to find a cheaper fare). But they can really only do this on flights from airports where there is relatively little competition (i.e. where there is a monopoly or perhaps an oligopoly).