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Suppose that there are 1million Federal workers at the lowest level of the federal bureaucracy and...

Suppose that there are 1million Federal workers at the lowest level of the federal bureaucracy and that above them are multiple layers of supervisors and supervisors of supervisors. Assume that each higher level is one-tenth of the size of the one below it because the government is using a 10:1 ratio of supervisee to supervisor. That is, for every 10 worker at the bottom, there is 1 supervisor; for every 10 of those supervisors, there is 1 supervisor; for everyone of those supervisors-of-supervisors, there is a supervisor of supervisors- of supervisors; and so on, all the way up the bureaucratic pyramid to the president.

a. How many supervisors will there be in each supervisory layer of the federal bureaucracy? Start with the layer of supervisors directly above the 1 million workers at the bottom.

b. How many supervisors are there in total at the level of the Federal bureaucracy pyramid, including the president?

c. If you count the 1 million workers at the bottom as the first layer of the federal bureaucracy, how many total layers are there, including the president?

d. How many federal employees are there in total at all layers including the president?

e. What fraction of all federal employees are supervisory, including the president?

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