I don't know about the M.B.A part; however, I can state that I have a good number of graduate students in the physics department that have a masters in computer science or engineering working on their PH. D. But many of them went into the workforce for a period after their B.S. and Master's programs. If I were to roughly guess though, it would near 6-12 years, excluding your undergrad work.
Note that my number of years is based on the assumed average time frame of getting a masters: 2-3 years. PHD work, consitering from the background I am assuming to get the MBA and then the Masters in Computer Sci, will likly take awhile since you would need to do some remedial work at the graduate level.
But I guess if you really had all of the background done in your undergrad, it could be possible.
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