"having the bikinis made in new york has made sense so far, but now that our sales volume has grown, it may make sense to export fabric to another country and then import the finished bikinis to the united states. i know what the respective costs are, but i have no idea what quality control will be like if i offshore production. which decision style is most appropriate for choosing a course of action? "

The answer would be Consultative Decision Making.

Explanation:

There are four types of decision making styles. Autocratic, with high leader power and low involvement of others. Consultative, with high leader power and high involvement of others. Delegating, with Low leader and others involvement. Fourth is Team, with high others involvement and low leader involvement.

In this type of scenario, the leader has to make a decision, so his power is high, and he needs the suggestions of the team members involved in the process, that means high involvement of team members as well. So Consultative Decision Making would be best in this type of decision making.