Assuming you had one, and a lab tech to operate it (lab techs still come as standard with the rest of the lab equipment, right? ), yeah it would be quite straightforward.
The handy part is that the main use of these machines is to represent the relative masses of different components in a sample by showing its "mass spectrum".
Since you know the structure of the compounds in the mixture, you know the relative proportions of the ions that form them, so you should be able to work out from the mass spectrum how much of each compound is in the mixture. The results from mass-spec are not really quantitative on their own so you still need to apply some chemistry-oriented thought to them, but with such a simple mixture it is quite straightforward.
Wikipedia has a good primer on the entire topic, but it does get a bit more technical than is really necessary at this level:
http://en.wikipedia.org/wiki/Mass_spectrometry