Problem 467. Mr. Pyramidad & Ms. Whissy Bolower

Businessman Mr. B. M. Pyramidad was drinking with his new girlfriend Ms. Whissy Bolower. He disclosed to her that he has an illegal business plan:

1. He, as Boss-I, will recruit x individuals as Operator-II,
2. Each of these operators will recruit x individuals at Helper-III,
3. Every helper must recruit x individuals as Peddler-IV.
4. All of them will be promoted to next higher level as soon as each of those peddlers deposit $1,000 cash to their acting Boss-I.
5. Then, whoever was the acting Boss-I, he or she must retire, but the business will continue to expand as usual.

Ms. Whissy Bolower has decided to blow the whistle. She is calculating that Mr. Pyramidad may come back at the Peddler-IV level after retiring. What could be the minimum x so he collects minimum y dollars net after retiring z times? Please try a general solution, the test suite may expand. For more information, see Pyramid Scheme.