Conditional MIN and RANK using dynamic array formulas

Hi,

I have a data set with a min_range and want to find the smallest values conditional on criteria_range1, criteria_range2 and criteria_range3. Then I want to rank the resulting smallest values in ascending order conditional on criteria_range1. The ranking must give the same rank to ties and then increase the next rank incrementally by 1. I want to accomplish this with a single formula that yields a dynamic array as output. Please see attached workbook.

Best regards,
Marbleking