I'm going to participate in a Summer School in Management for two weeks.
When applying for Schengen visa, should I put the main purpose of the journey as Study or Tourism/cultural because the period is short?
I would answer the question honestly. Instances of dishonestly on a visa application will hurt your credibility and cause the officers to wonder what else you aren't telling them. The primary purpose of your trip appears to be to take a class. Therefore you are traveling to study, even if only for a short period of time.
In your application, you can explain the nature and duration of the class.