Most of the Big 10 schools are really stingy with merit aid unless it comes from a named program. In comparison, the SEC gives a LOT more in scholarships based off GPA and SAT/ACT scores.
Also a point of caution regarding engineering and business - in most schools these are 4-year programs with a dedicated set of advisors, curriculum, clubs etc. and it is not easy to transfer majors at all unless you are prepared to start over as a freshman (as compared to transferring within the College of Arts & Sciences). Even smaller private schools like Northwestern have silo’ed off their business and engineering programs.
What a lot of people do in this case, is to take up Industrial and Systems Engineering instead, which in itself is a combination of business and engineering. Here is the list of prominent programs in Industrial Engineering. I would recommend looking at schools like NC State, Virginia Tech or Texas A&M which has a great program but also more merit aid compared to some of the other options on the list.