I am interested in doing a PhD in Industrial Engineering and Operations Research at any of the premier American Universities. I have a postgraduate degree in Industrial Engineering from Indian Institute of Technology, Kharagpur, India, which I completed in 1983. I have about 30 years of working experience in India as an Industrial Engineer.
Well, I was 58 when I applied for the Ph.D. program from which I received my doctorate, so the answer is yes.
Certainly you can. I personally believed that you will not only be competitive, but respected. My advice, apply, apply, and apply.
Certainly. It is not your age that matters, but the will to excel. Although rare, there are some who do pursue PhD past 50. I don't see why shouldn't you apply. If you are passionate about your aim, by all means go for it.