What is the minimum average appraisal score for all the managers in the company?

With 1 year of experience from 6 managers, one will have an appraisal score of 17 other five can have a score equal to 15.

=> Total score = 15*5+17 = 92

With 2 years of experience from 6 managers, one will have an appraisal score of 14 other five can have a score equal to 12.

=> Total score = 12*5+14 = 74

With 3 years of experience from 10 managers, one will have an appraisal score of 12 other nine can have a score equal to 10.

=> Total score = 10*9+12 = 102

With 4 years of experience from 5 managers, one will have an appraisal score of 13 other four can have a score equal to 10.

=> Total score = 10*4+13 = 53

Total score of all managers = 92+74+102+53 = 321

Total number of managers = 27

Therefore, the minimum average appraisal score for all the managers in the company = $$\ \frac{321}{27}$$ = 11.89

The answer is option A.