What strategic or commercial purposes did each of these capitals fulfill, and how would their locations have aided or hindered imperial administration?

The question is referring to the islamic capitals of the early modern era.

Explanation:

This capitals were: Istanbul, the capital of the Ottoman Empire, Isfahan, the capital of the Safavid Empire, and Delhi, the capital of the Mughal Empire.

The purpose of each of these capital was to centralize the administration of the empire.

Their locations would have helped the administration, especially in the case of Istanbul and Delhi, because of their central geographical location. As for Isfahan, it was also located in the center or the Safavid Empire, but in the middle of a very desertic and mountainous area, which made communications a little harder despite is central location.

it increase by 12% a year from 1812-1820