How much of the IE plan is business?

Not much more than other engineering majors. Some find it useful to complement their IE degree with marketing and management courses/modules, hence, they might choose them in their electives. 

What do IE's study?

The study plan contains core IE courses/modules that are mainly in the areas of manufacturing and materials science, optimization and simulation, systems and process engineering, and ergonomics. IE requires its students to maintain a strong understanding of basic calculus, statistics, programming, and basic sciences. 

Does IE mean work in factories?

IE teaches the mathematical and scientific bases for systems and processes to produce products and services. This is directly viewed in factories, and indirectly viewed in almost all other industries such as banks, airlines, hospitals, tech companies, etc. Therefore, IEs work and apply their knowledge in any industry where there is a process to be followed. 

Isn't IE essentially management or the business of engineering?

IE is still an engineering degree where students learn how to view systems and processes from a large picture perspective and solving its problems using statistical, optimization, and simulation methods. Due to their large picture ability, they sometimes take on management roles.